×

A bibliography on chromatic polynomials. (English) Zbl 0879.05034

Our intention is to make this bibliography as complete as possible and as such, some marginally related references are also included.

MSC:

05C15 Coloring of graphs and hypergraphs
01A70 Biographies, obituaries, personalia, bibliographies
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adam, A. A.; Broere, I., Chromatic polynomials of graphs in terms of trees, J. Math. Phys. Sci., 27, 231-240 (1993), MR95i: 05054 · Zbl 0806.05033
[2] Aigner, M., Graph Theory, (A Development From The 4-Color Problem (1987), BCS Associates: BCS Associates Moscow, Idaho USA), MR88b: 05001
[3] Akiyama, J.; Harary, F., A graph and its complement with specified properties VII: a survey, Theory and Application of Graphs, (Intern. Conf. on the Theory and Applications of Graphs (1980)), 1-12, MR84h: 05101b
[4] Arrowsmith, D. K.; Essam, J. W., Chromatic and flow polynomials for directed graphs, J. Combin. Theory Ser. B, 62, 349-362 (1994) · Zbl 0807.05031
[5] Athreya, K. B.; Pranesachar, C. R.; Singhi, N. M., On the number of Latin rectangles and chromatic polynomial of \(L(K_{r,s})\), Europ. J. Combin., 1, 9-17 (1980), MR82d: 05033 · Zbl 0461.05004
[6] Ayiguli, M.; Elkin, V. I., Chromatic classes of a class of 2-connected \((n, n + 2)\) graphs, (Natur. Sci., 10 (1993), J. Xinjiang Univ), 20-24, (Chinese, English and Chinese summaries). MR94d: 05051 · Zbl 0964.05510
[7] Baclawski, K., Homology and graphs, (Problémes Combinatoires et Thèorie des Graphes. Problémes Combinatoires et Thèorie des Graphes, Collq. Internat. CNRS, Orsay, 1976 (1978), CNRS: CNRS Paris), 17-18, MR80m: 05032
[8] Baker, G. A., Linked-cluster expansion for the graph-vertex coloration problem, J. Combin. Theory Ser. B, 10, 217-231 (1971), MR44: 3924 · Zbl 0175.50204
[9] Balasubramanian, K., Computational graph theory, (Proc. Graph Theory and Topology in Chemistry. Proc. Graph Theory and Topology in Chemistry, Conf. Athens, 51 (1987)), 514-528, MR89g: 92074
[10] Bao, X. W.; Chen, X. E., Chromaticity of the graph 0(a,b,c,e), J. Xinjiang Univ. Natur. Sci., 11, 19-22 (1994), (Chinese, English and Chinese summaries) · Zbl 0964.05511
[11] Bari, R. A., The four leading coefficients of the chromatic polynomials \(Q_n(u)\) and \(R_n(x)\) and the Birkhoff-Lewis conjecture, (Recent Progress in Combinatorics Proc. 3rd Waterloo Conf. on Combinatorics. Recent Progress in Combinatorics Proc. 3rd Waterloo Conf. on Combinatorics, 1968 (1969), Academic Press: Academic Press New York), 217-219, MR40: 5493
[12] Bari, R. A., Coefficients of \(u^{n−5}\) and \(u^{n−6}\) in the \(Q\)-chromial \(Qn (u)\), (Internat. Conf. on Combinatorial Mathematics. Internat. Conf. on Combinatorial Mathematics, 1970. Internat. Conf. on Combinatorial Mathematics. Internat. Conf. on Combinatorial Mathematics, 1970, Ann. New York Acad. Sci., 175 (1970)), 25-31, MR41: 8291 · Zbl 0227.05104
[13] Bari, R. A., Maximal \(m\)-gons in 4-regular major maps, (Recent Trends in Graph Theory. Recent Trends in Graph Theory, Lecture Notes in Math., Vol. 186 (1971), Springer: Springer Berlin), 5-8, MR44: 2638 · Zbl 0213.26101
[14] Bari, R. A., Minimal regular major maps with proper 4-rings, (Graph Theory and Applications. Graph Theory and Applications, Lecture Notes in Math., Vol. 303 (1972), Springer: Springer Berlin), 13-20, MR48: 10873
[15] Bari, R. A., Regular maps of at most 19 regions and their \(Q\)-chromials, J. Combin. Theory Ser. B, 12, 132-142 (1972), MR45: 3244 · Zbl 0211.56603
[16] Bari, R. A., Chromatically equivalent graphs, Graphs and Combinatorics, (Lecture Notes in Math., Vol. 406 (1974), Springer: Springer Berlin), 186-200, MR51: 232
[17] Bari, R. A., Chromatic polynomials and the internal and external activities of Tutte, (Graph Theory and Related Topics (1979), Academic Press: Academic Press New York), 41-52, MR81b: 05041 · Zbl 0472.05021
[18] Bari, R. A., Recent results on chromatically equivalent graphs, Ann. New York Acad. Sci., 319, 37-46 (1979), MR81f: 05074 · Zbl 0483.05027
[19] Bari, R. A., A combinatorial approach to graphical polynomials and spanning subgraphs, Ann. New York Acad. Sci., 328, 21-29 (1979), MR81f: 05075
[20] Bari, R. A., Line graphs and their chromatic polynomials, Ann. Discrete Math., 13, 15-21 (1982), MR83j: 05035 · Zbl 0495.05021
[21] Bari, R. A., Homomorphism polynomials of graphs, J. Combin. Inform. Systems Sci., 7, 56-64 (1982), MR84d: 05146 · Zbl 0494.05024
[22] Bari, R. A.; Crawford, C. G., Almost proper line colorings and near chromatic polynomials, (Graph Theory and Its Applications: East and West. Graph Theory and Its Applications: East and West, Ann. New York Acad. Sci., 576 (1989)), 42-50, MR92e: 05045 · Zbl 0793.05057
[23] Bari, R. A.; Crawford, C. G., New results in near-chromatic polynomials, (Graph Theory, Combinatorics, Algorithms, and Applications (1991), SIAM: SIAM Philadelphia, PA), 7-19, MR92m: 05078 · Zbl 0756.05052
[24] Bari, R. A.; Hall, D. W., Chromatic polynomials and Whitney’s broken circuits, J. Graph Theory, 1, 269-275 (1977), MR57: 16115 · Zbl 0387.05014
[25] Bari, R. A.; Kahn, X. Z., Chromatic equivalence and chromatic uniqueness, (Recent Studies in Graph Theory (1989)), 1-13, MR90m: 05053
[26] L.I. Basenshpiler, On chromatic polynomials of 2-isomorphic graphs, preprint.; L.I. Basenshpiler, On chromatic polynomials of 2-isomorphic graphs, preprint.
[27] Baxter, R. J., Chromatic polynomials of large triangular lattices, J. Phys. A: Math. Gen., 20, 5241-5261 (1987), MR89a: 82033 · Zbl 0625.05023
[28] Beck, I.; Krogdahl, S., On log concave sequences, Discrete Math., 94, 141-145 (1991), MR92h: 05011 · Zbl 0746.05006
[29] Behzad, M.; Chartrand, G., The line-chromatic polynomial of graph, Purtugaliae Math., 27, 31-41 (1968), MR41: 5242 · Zbl 0201.26102
[30] Behzad, M.; Chartrand, G.; Lesniak-Foster, L., Graphs and Digraphs (1979), Prindle, Weber & Schmidt: Prindle, Weber & Schmidt Boston, MA, MR80f: 05019 · Zbl 0403.05027
[31] Bender, E. A.; Goldman, J. R., On the application of Möbius inversion in combinatorial analysis, Amer. Math. Monthly, 82, 789-803 (1975), MR51: 12536 · Zbl 0316.05001
[32] Benzaquén, S.; Giudici, R., On \(k\)-regular graphs, (Report No. 91-08 (1991), Dpto. de Mat. puras y Aplicadas: Dpto. de Mat. puras y Aplicadas Simón Bolivar)
[33] Beraha, S., Infinite non-trivial families of maps and chromials, (Ph.D. Thesis (1975), Johns Hopkins University)
[34] S. Beraha, Concerning the chromatic coefficients of the main Lewis form, A.M.S. Abstracts 74T-A156.; S. Beraha, Concerning the chromatic coefficients of the main Lewis form, A.M.S. Abstracts 74T-A156.
[35] Beraha, S., Asymptotic formulae for BL regular maps, J. Combin. Inform. Systems Sci., 4, 6-13 (1979), MR80i: 05042 · Zbl 0402.05026
[36] Beraha, S., The Birkhoff-Lewis conjecture for families of chromials, J. Combin. Inform. Systems Sci., 4, 161-168 (1979), MR81d: 05028 · Zbl 0421.05027
[37] S. Beraha, Infinite non-trivial families of maps and chromials, Adv. Math., to appear.; S. Beraha, Infinite non-trivial families of maps and chromials, Adv. Math., to appear. · Zbl 0421.05027
[38] Beraha, S.; Kahane, J., Is the four-color conjecture almost false?, J. Combin. Theory Ser. B, 27, 1-12 (1979), MR80j: 05061 · Zbl 0331.05105
[39] S. Beraha, J. Kahane and R. Reid, \(B_7B_{10}\); S. Beraha, J. Kahane and R. Reid, \(B_7B_{10}\)
[40] Beraha, S.; Kahane, J.; Weiss, N. J., Limit of zeros of recursively defined polynomials, (Proc. Nat. Acad. Sci. USA, 72 (1975)), 4209, MR52: 5946 · Zbl 0315.30003
[41] Beraha, S.; Kahane, J.; Weiss, N. J., Limits of zeros of recursively defined families of polynomials, (Studies in Foundations and Combinatorics. Studies in Foundations and Combinatorics, Advances in Math., Supplementary Studies, Vol. 1 (1978)), 213-232, MR80c: 30005 · Zbl 0477.05034
[42] Beraha, S.; Kahane, J.; Weiss, N. J., Limit of chromatic zeros of some families of maps, J. Combin. Theory Ser. B, 28, 52-65 (1980), MR81f: 05076 · Zbl 0433.05030
[43] Berge, C., Graphs and Hypergraphs (1973), North-Holland: North-Holland Amsterdam, MR50: 9640 · Zbl 0483.05029
[44] Bergmann, H., Eine Färbungstheorie für endliche Graphen, J. Reine Angew. Math., 247, 87-91 (1971), MR43: 1884 · Zbl 0223.05102
[45] Berman, G., The dichromate and orientations of a graph, Canad. J. Math., 29, 947-956 (1977), MR57: 9591 · Zbl 0378.05031
[46] Berman, G.; Tutte, W. T., The golden root of a chromatic polynomial, J. Combin. Theory, 6, 301-302 (1969), MR39: 98 · Zbl 0174.26604
[47] Biggs, N. L., Expansions of the chromatic polynomial, Discrete Math., 6, 105-113 (1973), MR48: 1958 · Zbl 0271.05110
[48] Biggs, N. L., Algebraic Graph Theory (1994), Cambridge Univ. Press: Cambridge Univ. Press London, New York, MR95h: 05105 · Zbl 0501.05039
[49] Biggs, N. L.; Damerall, R. M.; Sands, D. A., Recursive families of graphs, J. Combin. Theory Ser. B, 12, 123-131 (1972), MR45: 3245 · Zbl 0215.05504
[50] Biggs, N. L.; Meredith, G. H.J., Approximations for chromatic polynomials, J. Combin. Theory Ser. B, 20, 5-19 (1976), MR52: 10469 · Zbl 0283.05102
[51] Birkhoff, G. D., The reducibility of maps, Amer. J. Math., 35, 115-128 (1912) · JFM 43.0575.01
[52] Birkhoff, G. D., A determinant formula for the number of ways of coloring a map, Ann. Math., 14, 2, 42-46 (1912) · JFM 43.0574.02
[53] Birkhoff, G. D., On the number of ways of coloring a map, (Proc. Edinburgh Math. Soc. (1930)), 83-91, (2) · JFM 56.0499.02
[54] Birkhoff, G. D., On the polynomial expressions for the number of ways of coloring a map, (Annali della R. Scuola Normale Superiore di Pisa. Annali della R. Scuola Normale Superiore di Pisa, Scienze Fisiche e Matematiche, 3 (1934)), 1-19, (2) · JFM 60.0501.06
[55] Birkhoff, G. D.; Lewis, D., Chromatic polynomials, Trans. Amer. Math. Soc., 60, 355-451 (1946), MR8: 284f · Zbl 0060.41601
[56] Bjorner, A., The unimodality conjecture for convex polytopes, Bull. Amer. Math. Soc., 4, 187-188 (1981), MR82b: 52013 · Zbl 0458.52004
[57] Blass, A.; Sagan, B. E., Bijective proofs of two broken circuit theorems, J. Graph Theory, 10, 15-21 (1986), MR87e: 05066 · Zbl 0592.05022
[58] Bondy, J. A.; Hemminger, R. L., Graph reconstruction — a survey, J. Graph Theory, 1, 227-268 (1977), MR58: 372 · Zbl 0375.05040
[59] Bondy, J. A.; Murty, U. S.R., Graph Theory with Applications (1976), Elsevier: Elsevier New York, MR54: 117 · Zbl 1134.05001
[60] Borodin, O. V.; Dmitriev, I. G., Siberian Math. J., 32, 17-21 (1991), MR92g: 05088 · Zbl 0742.05078
[61] Borowiecki, M., Two external problems in the class of uniquely colourable graphs, Graphs Hypergraphs and Matriods II, Zielona Góra 1987, (Proc. 6th Regional Scientific Session of Mathematicians. Proc. 6th Regional Scientific Session of Mathematicians, Źagań, June 1986 (1987)), 17-25
[62] Borowiecki, M., Problem 2, Graphs, Hypergraphs and Matriods III, Zielona Góra, (Proc. 7th Regional Scientific Session of Mathematicians. Proc. 7th Regional Scientific Session of Mathematicians, Kalsk, September 1988 (1989)), 187-190
[63] Borowiecki, M.; Drgas-Burchardt, E., Classes of chromatically unique graphs, Discrete Math., 111, 71-75 (1993), MR93j: 05054 · Zbl 0788.05040
[64] Borowiecki, M.; Drgas-Burchardt, E., Classes of chromatically unique or equivalent graphs, Discrete Math., 121, 11-18 (1993), MR94f: 05051 · Zbl 0782.05030
[65] Borowiecki, M.; Patil, H. P., On colouring and the chromatic polynomial of \(k\)-trees, J. Combin. Inform. System Sci., 11, 124-128 (1986), MR89j: 05035 · Zbl 0692.05031
[66] Braun, K.; Kretz, M.; Walter, B.; Walter, M., Die chromatischen Polynome unterringfreier Graphen, Manuscripta Math., 14, 223-234 (1974), MR50: 6906 · Zbl 0293.05113
[67] Brenti, F., Expansions of chromatic polynomials and log-concavity, Trans. Amer. Math., 332, 729-756 (1992), MR93j: 05055 · Zbl 0757.05052
[68] Brenti, F., Permutation enumeration symmetric functions, and unimodality, Pacific J. Math., 157, 1-28 (1993), (English summary). MR94g: 05096 · Zbl 0805.05089
[69] Brenti, F.; Royle, G. F.; Wagner, D. G., Location of zeros of chromatic and related polynomials of graphs, Canad. J. Math., 46, 55-80 (1994), MR94k: 05077 · Zbl 0804.05034
[70] Brito, M. R., On supercycle \(C(a,b,c)\), Ars Combin., 25A, 165-171 (1988), MR89f: 05074 · Zbl 0658.05030
[71] Brylawski, T., Reconstructing combinatorial geometries, (Graphs and Combinatorics Proc. Capital Conf. on Graph Theory and Combinatorics. Graphs and Combinatorics Proc. Capital Conf. on Graph Theory and Combinatorics, George Washington Univ., 1973. Graphs and Combinatorics Proc. Capital Conf. on Graph Theory and Combinatorics. Graphs and Combinatorics Proc. Capital Conf. on Graph Theory and Combinatorics, George Washington Univ., 1973, Lecture Notes in Math., Vol. 406 (1974), Springer: Springer Berlin), 226-235, MR51: 5345 · Zbl 0224.05007
[72] Brylawski, T., Intersection theory for graphs, J. Combin. Theory Ser. B, 30, 233-246 (1981), MR82g: 05036 · Zbl 0463.05031
[73] Caccetta, L.; Foldes, S., Symmetric calculation of chromatic polynomials, Ars Combin., 4, 289-292 (1977), MR58: 10558 · Zbl 0396.05016
[74] Capobianco, M.; Molluzzo, J. C., Examples and Counterexamples in Graph Theory (1978), North-Holland: North-Holland Amsterdam, MR58: 10536 · Zbl 0369.05021
[75] Cayley, A., (Proc. Royal Geographical Soc., 1 (1879)), 259 · JFM 02.0845.01
[76] Cerasoli, M.; Eugeni, F., On the chromatic polynomial of a graph, Ricerca: Mat. Pure Appl., 31, 5-10 (1980), MR85i: 05104
[77] Chalcraft, D. A., Certain graph invariants do not distinguish all graphs, J. Graph Theory, 14, 341-346 (1990), MR91g: 05045 · Zbl 0705.05055
[78] Chandrasekharan, N.; Lasker, R.; Veni Madhaven, C. E., Chromatic polynomials of chordal graphs, (Congr. Numer., 61 (1988)), 133-142, MR89h: 05028
[79] Chao, C. Y.; Chen, Z., On uniquely 3-colorable graphs, Discrete Math., 112, 21-27 (1993), MR94e: 05207 · Zbl 0780.05021
[80] Chao, C. Y.; Guo, Z.-Y.; Li, N.-Z., Some families of chromatically equivalent graphs, Bull. Malaysian Math. Soc. (Second Ser.), 15, 77-82 (1992), MR94b: 05076 · Zbl 0782.05031
[81] C.Y. Chao, Z.-Y. Guo and N.-Z. Li, On \(q\); C.Y. Chao, Z.-Y. Guo and N.-Z. Li, On \(q\)
[82] Chao, C. Y.; Li, N.-Z., On trees of polygons, Arch. Math. (Basel), 45, 180-185 (1985), MR87b: 05111 · Zbl 0575.05027
[83] Chao, C. Y.; Li, N.-Z.; Xu, S.-J., On \(q\)-trees, J. Graph Theory, 10, 129-136 (1986), MR87e: 05068 · Zbl 0591.05021
[84] Chao, C. Y.; Novacky, G. A., On maximally saturated graphs, Discrete Math., 41, 139-143 (1982), MR85a: 05035 · Zbl 0495.05023
[85] Chao, C. Y.; Whitehead, E. G., On chromatic equivalence of graphs, (Theory and Applications of Graphs. Theory and Applications of Graphs, Lecture Notes in Math., Vol. 642 (1978), Springer: Springer Berlin), 121-131, MR85: 21753
[86] Chao, C. Y.; Whitehead, E. G., Chromatically unique graphs, Discrete Math., 27, 171-177 (1979), MR80m: 05036 · Zbl 0411.05035
[87] Chao, C. Y.; Whitehead, E. G., Chromaticity of self-complementary graphs, Arch. Math. (Basel), 32, 295-304 (1979), MR81c: 05039 · Zbl 0395.05031
[88] Chao, C. Y.; Zhao, L.-C., Chromatic polynomials of a family of graphs, Ars Combin., 15, 111-129 (1983), MR85d: 05110 · Zbl 0532.05027
[89] Chao, C. Y.; Zhao, L.-C., A note concerning chromatic polynomials, Discrete Math., 45, 127-128 (1983), MR84f: 05041 · Zbl 0507.05033
[90] Chao, C. Y.; Zhao, L.-C., Chromatic polynomials of connected graphs, Arch. Math. (Basel), 43, 187-192 (1984), MR86b: 05028 · Zbl 0535.05053
[91] Chee, Y. M.; Royle, G. F., The chromaticity of a class of \(K_5\)-homeomorphs (1990), preprint
[92] Chen, X. E., Further discussions on \(q\)-graphs, J. Xinjiang Univ., 10, 25-27 (1993), (Chinese, English summary). MR94h: 05065 · Zbl 1056.05533
[93] Chen, X. E.; Bao, X. W.; Ouyang, K. Z., Chromaticity of the graph \(θ(a,b,c,d)\), J. Shanxi Normal Univ., 20, 75-79 (1992), (Chinese, English summary)
[94] Chen, X. E.; Ouyang, K. Z., Chromaticity of some 2-connected \((n,n + 2)\)-graphs, J. Lanzhou Univ. (Natural Sciences), 28, 183-184 (1992)
[95] Chia, G. L., A note on chromatic uniqueness of graphs, J. Graph Theory, 10, 541-543 (1986), MR88e: 05038 · Zbl 0616.05035
[96] Chia, G. L., Some remarks on the chromatic uniqueness of graphs, Ars Combin., 26A, 65-72 (1988), MR90j: 05065 · Zbl 0672.05033
[97] Chia, G. L., The Petersen graph is uniquely determined by its chromatic polynomial, (Research Report No. 31/88 (1988), Dept. of Mathematics, Univ. Malaya)
[98] Chia, G. L., The chromaticity of wheels with a missing spoke, Discrete Math., 82, 209-212 (1990), MR91i: 05054 · Zbl 0712.05025
[99] Chia, G. L., On the join of graphs and chromatic uniqueness, J. Graph Theory, 19, 251-261 (1995), MR96b: 05060 · Zbl 0819.05027
[100] Chia, G. L., On chromatic uniqueness of graphs with connectivity two, Malaysian J. Sci., 16B, 61-65 (1995)
[101] Chia, G. L., The chromaticity of wheels with a missing spoke, II, Discrete Math., 148, 305-310 (1996) · Zbl 0838.05052
[102] G.L. Chia, On the chromatic equivalence class of a family of graphs, Discrete Math., to appear.; G.L. Chia, On the chromatic equivalence class of a family of graphs, Discrete Math., to appear. · Zbl 0869.05031
[103] G.L. Chia, On the chromatic equivalence class of graphs, Discrete Math., to appear.; G.L. Chia, On the chromatic equivalence class of graphs, Discrete Math., to appear. · Zbl 0918.05048
[104] Chia, G. L.; Goh, B. H.; Koh, K. M., The chromaticity of some families of complete tripartite graphs, Scientia, Ser. A, 2, 27-37 (1988), (Special issue of Scientia in honour of Prof. Roberto W. Frucht.) · Zbl 0760.05037
[105] Chvátal, V., A note on coefficients of chromatic polynomials, J. Combin. Theory, 9, 95-96 (1970), MR41: 8293 · Zbl 0203.56603
[106] Chvátal, V., (Problem 9, Hypergraph Seminar. Problem 9, Hypergraph Seminar, Lecture Notes in Math., Vol. 411 (1974), Springer: Springer Berlin), 281
[107] Cortez Morales, W. J., On chromatic polynomials, Revista de Matematica e Estatistica, 6, 59-66 (1988), MR90d: 05096 · Zbl 0689.05023
[108] Crapo, H. H., A higher invariant for matroids, J. Combin. Theory, 2, 406-417 (1967), MR35: 6579 · Zbl 0168.26203
[109] Crapo, H. H., The Tutte polynomial, Aequationes Math., 3, 211-229 (1969), MR41: 6705 · Zbl 0197.50202
[110] Crapo, H. H., Chromatic polynomials for a join of graphs, Colloquia Math. Soc. Janos. Bolyai, 4, 239-245 (1969), MR45: 8572
[111] Crapo, H. H., Numerical invariants of geometries and graphs, (Proc. 25th Summer Meeting, Canad. Math. Congress (1971), Lakehead University), 42-54, MR50: 12781
[112] Dhurandhar, M., Characterization of quadratic and cubic \(σ\)-polynomials, J. Combin. Theory Ser. B, 37, 210-220 (1984), MR86f: 05061 · Zbl 0554.05030
[113] Dmitriev, I. G., Metody Diskret. Analiz. Vyp., 38, 9-18 (1982), MR85c: 05016 · Zbl 0531.05046
[114] Dohmen, K., Chromatische Polynome von Graphen und Hypergraphen, (Dissertation (1993), Universität Düsseldorf) · Zbl 0837.05057
[115] Dohmen, K., Lower bounds and upper bounds for chromatic polynomials, J. Graph Theory, 17, 75-80 (1993), MR94e: 05103 · Zbl 0780.05023
[116] Dohmen, K., A broken-circuits-theorem for hypergraphs, Arch. Math. (Basel), 64, 159-162 (1995) · Zbl 0813.05048
[117] Dong, F. M., On the uniqueness of chromatic polynomial of generalized wheel graph, J. Math. Res. Exposition, 10, 447-454 (1990), (Chinese, English summary). MR91i: 05055 · Zbl 0774.05038
[118] Dong, F. M., The chromatic uniqueness of two classes of special graphs, Acta Math. Sinica, 34, 242-251 (1991), (Chinese). MR92i: 05092 · Zbl 0753.05034
[119] Dong, F. M., On chromatic uniqueness of two infinite families of graphs, J. Graph Theory, 17, 387-392 (1993), MR94c: 05032 · Zbl 0777.05059
[120] Dong, F. M.; Koh, K. M., On the structure and chromaticity of the graphs in which any two colour classes induce a tree (1994), preprint · Zbl 0893.05004
[121] Dong, F. M.; Koh, K. M., On graphs in which any pair of colour classes but one induces a tree (1994), preprint · Zbl 0874.05023
[122] Dong, F. M.; Liu, Y. P., All wheels with two missing consecutive spokes are chromatically unique (1993), preprint · Zbl 0957.05043
[123] Dong, F. M.; Liu, Y. P., On the chromatic uniqueness of the graph \(W(n,n\) − 2) + \(K_k\), Discrete Math., 145, 95-103 (1995) · Zbl 0837.05055
[124] F.M. Dong and Y.P. Liu, On the chromatic uniqueness of the graph \(Wnnk\); F.M. Dong and Y.P. Liu, On the chromatic uniqueness of the graph \(Wnnk\) · Zbl 0857.05039
[125] Dong, F. M.; Liu, Y. P.; Koh, K. M., The chromaticity of odd wheels with a missing spoke (1994), preprint · Zbl 0880.05038
[126] Dowling, T. A., Codes, packings and critical problem, (Atti del Copnvegno di Geometria e sue applicazioni. Atti del Copnvegno di Geometria e sue applicazioni, Perugia 1970, Ist. Mat. (1971), Univ. Perugia), 209-224, MR49: 2438 · Zbl 0276.05025
[127] Du, Q. Y., Chromatic polynomials of triangulated graphs, Nei Mongol Daxue Xuebao Ziran Kexue, 23, 148-151 (1992), (Chinese, English summary). MR93a: 05060 · Zbl 1333.05108
[128] Du, Q. Y., On σ-polynomials and a class of chromatically unique graphs, Discrete Math., 115, 153-165 (1993), MR94e: 05104 · Zbl 0774.05039
[129] Du, Q. Y., A partial ordering of the σ-polynomials, Neimenggu Daxue Xuebao Ziran Kexue, 24, 563-566 (1993), (Chinese, English and Chinese summaries). MR94k: 05078 · Zbl 1333.05107
[130] Du, Q. Y., New upper bounds for the coefficients of σ-polynomials, Neimenggu Daxue Xuebao Ziran Kexue, 25, 14-16 (1994), (Chinese, English and Chinese summaries). MR94k: 05102 · Zbl 1333.05150
[131] Du, Q. Y., Chromaticity of the complement of paths and cycles (1994), preprint
[132] Du, Q. Y., On σ-equivalence and χ-equivalence of graphs, J. Graph Theory, 21, 211-217 (1996) · Zbl 0838.05050
[133] Eisenberg, B., On the coefficients of the chromatic polynomial of a graph, (Ph.D. Thesis (1970), Adelphi University)
[134] Eisenberg, B., Generalized lower bounds for the absolute values of the coefficients of chromatic polynomials, (Lecture Notes in Math., Vol. 186 (1971), Springer: Springer Berlin), 85-94, MR43: 6133
[135] Eisenberg, B., An interpretation of the chromatic polynomial for some negative arguments, (Proc. 3rd Southern Conf. on Combinatorics, Graph Theory and Computing (1972)), 197-204, MR50: 157
[136] Eisenberg, B., Characterization of a tree by means of coefficients of the chromatic polynomial, Trans. New York Acad. Sci., 34, 146-153 (1972), MR55: 2635
[137] Eisenberg, B., Characterization of a polygonal graph by means of its chromatic polynomial, (Proc. 4th Southern Conf. on Graph Theory and Computing. Proc. 4th Southern Conf. on Graph Theory and Computing, Utilitas Math. (1973)), 275-278, MR50: 1951
[138] Enting, I. G., The combinatorics of algebraic graph theory in theoretical physics, (Lecture Notes in Math., Vol. 686 (1978), Springer: Springer Berlin), 148-156, MR80d: 82001 · Zbl 0397.05051
[139] Essam, J. W., Graph theory and statistical physics, Discrete Math., 1, 83-112 (1971/1972), MR45: 6336 · Zbl 0213.26102
[140] Farr, G. E., A correlation inequality involving stable set and chromatic polynomials, J. Combin. Theory Ser. B, 58, 14-21 (1993), MR94a: 05177 · Zbl 0733.05038
[141] Farrell, E. J., On a general class of graph polynomials, J. Combin. Theory Ser. B, 26, 111-122 (1979), MR81a: 05109 · Zbl 0328.05006
[142] Farrell, E. J., An introduction to matching polynomials, J. Combin. Theory Ser. B, 27, 75-86 (1979), MR81a: 05110 · Zbl 0335.05131
[143] Farrell, E. J., Chromatic roots — some observations and conjectures, Discrete Math., 29, 161-171 (1980), MR81c: 05040 · Zbl 0443.05040
[144] Farrell, E. J., On chromatic coefficients, Discrete Math., 29, 257-264 (1980), MR81d: 05029 · Zbl 0443.05041
[145] Farrell, E. J., A result on co-chromatic graphs, Internat. J. Math. and Math. Sci., 4, 365-369 (1981), MR82d: 05059 · Zbl 0457.05031
[146] Farrell, E. J., A generalization of the dichromatic polynomials of a graph, J. Math. and Math. Sci., 4, 725-729 (1981), MR83g: 05033 · Zbl 0476.05071
[147] Farrell, E. J., On a class of polynomials associated with the subgraphs of a graph and its application to chromatic and dichromatic polynomials, Bull. Austral. Math., 26, 343-354 (1982), MR84b: 05082 · Zbl 0504.05057
[148] Farrell, E. J., A graph-theoretic approach to rook theory, Caribbean J. Math., 7, 47 (1988), MR94c: 05057 · Zbl 0776.05085
[149] Farrell, E. J., The derivative of the chromatic polynomial, (Proc. 6th Caribbean Conf. on Combin. and Comput. (1991)), 145-157 · Zbl 0476.05047
[150] Farrell, E. J., The impact of \(F\)-polynomials in graph theory, Ann. Discrete Math., 55, 173-178 (1993), MR93k: 05003 · Zbl 0786.05064
[151] Farrell, E. J.; Guo, J. M.; Constantine, G. M., On matching coefficients, Discrete Math., 89, 203-210 (1991), MR92d: 05124 · Zbl 0764.05074
[152] Farrell, E. J.; Wahid, S. A., The chromatic polynomial as the determinant of a matrix, (Proc. 6th Caribbean Conf. on Combin. and Comput. (1991)), 168-176 · Zbl 0938.05051
[153] Farrell, E. J.; Whitehead, E. G., On matching and chromatic properties of circulants, J. Combin. Math. Combin. Comput., 8, 79-88 (1990), MR91j: 05080 · Zbl 0747.05068
[154] Farrell, E. J.; Whitehead, E. G., Matching, rook and chromatic polynomials and chromatically vector equivalent graphs, J. Combin. Math. Combin. Comput., 9, 107-118 (1991), MR92b: 05037 · Zbl 0783.05048
[155] Farrell, E. J.; Whitehead, E. G., Connections between matching and chromatic polynomials, Internat. J. Math. and Math. Sci., 15, 757-766 (1992), MR93h: 05125 · Zbl 0799.05053
[156] Ferch, H.; Richmond, L. B., A numerical study of chromatic polynomials, (Congr. Numer., 18 (1977)), 367-379, MR80j: 05062 · Zbl 0474.05027
[157] Figueroa-Centeno, R. M.; Giudici, R. E., An improved algorithm for the chromatic polynomial, (Report No. 1-89 (1989), Escula de Matemáticas, Universidad Metropolitana)
[158] Figueroa-Centeno, R. M.; Giudici, R. E., Frucht’s algorithm for the chromatic polynomial, (Proc. 6th Caribbean Conf. on Combin. and Comput., 6 (1991)), 177-184
[159] Foldes, S., The rotor effect can alter the chromatic polynomial, J. Combin. Theory Ser. B, 25, 237-239 (1978), MR80c: 05070 · Zbl 0325.05105
[160] S. Foldes, Hypergraph chromatic polynomials, Research Report CORR 79-20, Faculty of Mathematics, University of Waterloo.; S. Foldes, Hypergraph chromatic polynomials, Research Report CORR 79-20, Faculty of Mathematics, University of Waterloo. · Zbl 0396.05016
[161] Fortuin, C. M.; Kasteleyn, P. W., On the random-cluster model. I, Introduction and relation to other models, Physica, 57, 536-564 (1972), MR50: 12107
[162] Frank, S.; Shier, D., The chromatic polynomial revisited, (Congr. Numer., 55 (1986)), 57-68, MR88d: 05059 · Zbl 0645.05038
[163] Frucht, R. W., A new method of computing chromatic polynomials of graphs, (Analysis, Geometry, and Probability. Analysis, Geometry, and Probability, Lecture Notes in Pure and Appl. Math., Vol. 96 (1985), Dekker: Dekker New York), 69-77, MR86i: 05058
[164] Frucht, R. W.; Giudici, R. E., Some chromatically unique graphs with seven points, Ars Combin., 16A, 161-172 (1983), MR85d: 05114 · Zbl 0536.05026
[165] Frucht, R. W.; Giudici, R. E., A note on the matching numbers of triangle-free graphs, J. Graph Theory, 9, 455-458 (1985), MR88d: 05132 · Zbl 0664.05046
[166] Gernert, D., Recent results on chromatic polynomials, Contributions to Operations Research and Mathematical Economics, Vol. 1, 307-314 (1984), Methoda Oper. Res. 51 Athena̋um/Hanstein, Kőnigstein/Ts. MR86g: 05033 · Zbl 0546.05028
[167] Gernert, D., A survey of partial proofs for Read’s conjecture and some recent results, Methods Oper. Res., 49, 233-238 (1985), MR87a: 05068 · Zbl 0582.05027
[168] Girse, R. D., Chromatic polynomials for certain unlabeled graphs, J. Combin. Inform. Systems Sci., 10, 151-156 (1985), MR89j: 05036 · Zbl 0695.05020
[169] Giudici, R. E., Formas recursivas para los polinomios cromaticos de los prismas y sus asociados, (Report No. 76 (1982), Dpto. de Mat. y Ciencia de la Comp. Univ. Simón Bolivar)
[170] Giudici, R. E., Some new families of chromatically unique graphs, Analysis, Geometry, and Probability, (Lecture Notes in Pure and Appl. Math., Vol. 96 (1985), Dekker: Dekker New York), 147-158, MR86i: 05059
[171] Giudici, R. E., A note on chromatic equivalence of graphs (1988), Scientia, Valparaiso: Scientia, Valparaiso Chile
[172] Giudici, R. E.; Lima de Sá, Chromatic uniqueness of certain bipartite graphs, (Congr. Numer., 76 (1990)), 69-75, MR92i: 05094 · Zbl 0862.05045
[173] Giudici, R. E.; López, M. A., Chromatic uniqueness of \(sKn\), (Report No. 85-03 (1985), Dpto. de Mat. y Ciencia de la Comp. Univ. Simón Bolivar)
[174] Giudici, R. E.; López, M. A.; Salzberg, P. M., Chromatic uniqueness for some bipartite graphs \(K_{m,n}\), Acta Cient. Venezolana, 37, 484-494 (1986), (Spanish, English summary), MR88i: 05080 · Zbl 0617.05028
[175] Giudici, R. E.; Margaglio, C., Chromatically equivalent graphs, Ars Combin., 25B, 221-229 (1988), MR89k: 05036 · Zbl 0665.05018
[176] Giudici, R. E.; Margaglio, C., Chromaticity of supercycles of four cells, (Proc. 6th Caribbean Conf. on Combin. and Comput., 6 (1991)), 185-198
[177] Giudici, R. E.; Melián, M. Y., Chromatic uniqueness of 3-face graphs, (Report No. 88-05 (1988), Dpto. de Mat y Ciencia de la Comp., Univ. Simón Bolivar)
[178] Giudici, R. E.; Melián, M. Y., Chromatic uniqueness of the supercycle \(C(b,a,a,a)\), (Report No. 3-88 (1988), Escuela de Matemáticas, Universidad Metropolitana)
[179] Giudici, R. E.; Vinkle, R. M., A table of chromatic polynomials, J. Combin. Inform. Systems Sci., 5, 323-350 (1980), MR82f: 05039 · Zbl 0454.05026
[180] Goldman, J. R.; Joichi, J. T.; White, D. E., Rook theory III. Rook polynomials and the chromatic structure of graphs, J. Combin. Theory Ser. B, 25, 135-142 (1978), MR58: 27526a · Zbl 0336.05005
[181] Gracia, Z.; Salzberg, P. M., Chromatic classification of \(K_p\) — \(G_6\), Ars Combin., 20B, 107-111 (1985), MR87g: 05094 · Zbl 0609.05035
[182] Grimmett, G. R., Random graph theorems, (Trans. 7th. Prague Conf. on Inform. Theory, Statistical Decision Functions, Random Processes and of the 8th. European Meeting of Statisticians. Trans. 7th. Prague Conf. on Inform. Theory, Statistical Decision Functions, Random Processes and of the 8th. European Meeting of Statisticians, Tech. Univ., Prague, Prage 1974 (1977), Riedel: Riedel Dordrecht), MR58: 27644 · Zbl 0565.90017
[183] Grimmett, G. R., The rank polynomials of large random lattices, J. London Math. Soc., 18, 2, 567-575 (1978), MR80a: 60129 · Zbl 0398.05009
[184] Guo, Z. Y.; Li, N. Z., The \(m\)-clique polynomial and its application to chromatic polynomials, (Graph Theory, Combinatorics, Algorithms, and Applications (1991), SIAM: SIAM Philadelphia), 331-341, MR92k: 05126 · Zbl 0751.05038
[185] Guo, Z. Y.; Li, Y. J., Chromatic uniqueness of complement of the cycles union, Kexue Tongbao, 33, 1676 (1988)
[186] Guo, Z. Y.; Li, Y. J., Chromatic uniqueness of complement of the cycles union, J. Wuhan Urban Construction Inst., 6, 1-9 (1989), (Chinese, English summary)
[187] Haggard, G., Excursions in Graph Theory (1980), University of Maine: University of Maine Orono, MR82m: 0500 · Zbl 0444.05036
[188] Haggard, G., Computing chromatic polynomials of large graphs, I, J. Combin. Math. Combin. Comput., 13, 175-186 (1993), MR94a: 05074 · Zbl 0830.05030
[189] Haggard, G., Computing chromatic polynomials of large graphs, II, Isomorphism abstract data type for small graphs, Caribbean J. Math. Comput. Sci., 3, 35-43 (1993) · Zbl 0842.05036
[190] Hall, D. W., On golden identities for constrained chromials, J. Combin. Theory Ser. B, 11, 287-298 (1971), MR44: 6510 · Zbl 0203.56604
[191] Hall, D. W., Chromatic polynomials and graph coloring, N.Y. State Math. Teachers J., 23 (1973)
[192] Hall, D. W., Coloring seven-circuits, (Lecture Notes in Math., Vol. 406 (1974), Springer: Springer Berlin), 273-290, MR51: 5366
[193] Hall, D. W., Rochromials and the colourings of circuits, (Graph Theory and Related Topics Proc. Conf. Univ. Waterloo. Graph Theory and Related Topics Proc. Conf. Univ. Waterloo, 1977 (1979), Academic Press: Academic Press New York), 233-245, MR80j: 05063
[194] Hall, D. W.; Lewis, D. C., Coloring six-rings, Trans. Amer. Math. Soc., 64, 184-191 (1948), MR10: 136g · Zbl 0033.13801
[195] Hall, D. W.; Siry, J. W.; Vanderslice, B. R., The chromatic polynomial of the truncated icosahedron, (Proc. Amer. Math. Soc., 16 (1965)), 620-628, MR31: 3361 · Zbl 0132.20702
[196] Han, B. T., The chromaticity of graphs \(K_n(1, m)\), Acta Math. Appl. Sinica, 9, 101-112 (1986) · Zbl 0593.05028
[197] Han, B. T., Chromaticity of \(q_k\)-trees, Acta Math. Appl. Sinica, 11, 457-467 (1988), (Chinese, English summary). MR90a: 05083 · Zbl 0666.05032
[198] Hanlon, P., The chromatic polynomial of an unlabeled graph, J. Combin. Theory Ser. B, 38, 226-239 (1985), MR86i: 05080 · Zbl 0567.05025
[199] Harary, F., Graph Theory (1969), Addison-Wesley: Addison-Wesley Reading, MA, MR41: 1566 · Zbl 0797.05064
[200] N. Hartsfield, The chromatic polynomial of the complete bipartite graph, preprint.; N. Hartsfield, The chromatic polynomial of the complete bipartite graph, preprint. · Zbl 0697.05021
[201] Helgason, T., On geometric hypergraphs, (Proc. 2nd Chapel Hill Conf. on Combinatorial Mathematics and its Applications (1970), Univ. North Carolina: Univ. North Carolina Chapel Hill), 276-284, MR42: 1714 · Zbl 0209.55203
[202] Heron, A. P., Matroid polynomials, (Combinatorics Proc. Conf. Combinatorial Math.. Combinatorics Proc. Conf. Combinatorial Math., Math. Inst. Oxford, 1972 (1972), Inst. Math. Appl: Inst. Math. Appl Southend-on-Sea), 164-202, MR49: 4814
[203] Hoggar, S. G., Chromatic polynomials and logarithmic concavity, J. Combin. Theory Ser. B, 16, 248-254 (1974), MR49: 7170 · Zbl 0268.05104
[204] Hoggar, S. G., Chromatic polynomials and broken cycles, J. Combin. Theory Ser. B, 19, 77-86 (1975), MR53: 5353 · Zbl 0281.05102
[205] Hong, Y., A note on the coefficients of chromatic polynomials, (J. East China Norm. (1984), Univ. Natur. Sci. Ed), 33-35, MR89i: 05117 · Zbl 0576.05026
[206] Jackson, B., A zero-free interval for chromatic polynomials of graphs, Combin. Prob. Comput., 2, 325-336 (1993), MR94m: 05082 · Zbl 0794.05030
[207] D.M. Jackson, The lattices of partitions and non-crossing partitions, and the Birkhoff-Lewis equations for chromatic polynomial of a planar map, Research Report CORR 89-34, Faculty of Mathematics, University of Waterloo.; D.M. Jackson, The lattices of partitions and non-crossing partitions, and the Birkhoff-Lewis equations for chromatic polynomial of a planar map, Research Report CORR 89-34, Faculty of Mathematics, University of Waterloo.
[208] Jaeger, F., On Tutte polynomials and cycles of plane graphs, J. Combin. Theory Ser. B, 44, 127-146 (1988), MR89b: 05086 · Zbl 0595.05033
[209] Jensen, T. R.; Toft, B., Graph Colouring Problems (1995), Wiley: Wiley New York, MR 95h: 05067 · Zbl 0971.05046
[210] Jones, R. P., Hereditary properties of \(P\)-chromatic numbers, (Combinatorics Proc. British Combinatorial Conf.. Combinatorics Proc. British Combinatorial Conf., Univ. College Wales Aberystwyth 1973 (1974), C.U.P: C.U.P London), 83-88, MR52: 5464
[211] Joyce, D., Generalized chromatic polynomials, Discrete Math., 50, 51-62 (1984), MR85e: 05009 · Zbl 0543.05029
[212] Kahn, S., Chromatic equivalence and chromatic uniqueness, (Doctoral Dissertation (1980), George Washington University)
[213] Kim, D.; Enting, I. G., The limit of chromatic polynomials, J. Combin. Theory Ser. B, 26, 327-336 (1979), MR81b: 05047 · Zbl 0417.05028
[214] Koh, K. M.; Goh, B. H., Two classes of chromatically unique graphs, Discrete Math., 82, 13-24 (1990), MR91i: 05058 · Zbl 0697.05027
[215] Koh, K. M.; Teo, C. P., The chromatic uniqueness of graphs related to broken wheels, (Research Report 413 (1990), Math. Dept., National Univ. of Singapore) · Zbl 0752.05029
[216] Koh, K. M.; Teo, C. P., Some results on chromatically unique graphs, (Proc. Asian Math. Conf. (1990)), 258-262, MR93b: 00022 · Zbl 0940.05502
[217] Koh, K. M.; Teo, C. P., The chromatic uniqueness of certain broken wheels, Discrete Math., 96, 65-69 (1991), MR92i: 05096 · Zbl 0752.05029
[218] Koh, K. M.; Teo, C. P., Chromatic equivalence of a graph and its complement, Bull. Inst. Combin. Appl., 3, 81-82 (1991), MR93e: 05032 · Zbl 0829.05031
[219] Koh, K. M.; Teo, C. P., Chromaticity of series-parallel graphs, Discrete Math., 154, 289-295 (1996) · Zbl 0856.05035
[220] Koh, K. M.; Teo, K. L., The search for chromatically unique graphs, Graphs Combin., 6, 259-285 (1990), MR91k: 05044 · Zbl 0727.05023
[221] Koh, K. M.; Teo, K. L., Chromatic classes of 2-connected \((n, n+3)\)-graphs with at least two triangles, Discrete Math., 127, 243-258 (1994), MR95b: 05078 · Zbl 0796.05033
[222] Korfhage, P. R., σ-polynomials and graph colorings, J. Combin. Theory Ser. B, 24, 137-152 (1978), MR58: 10564 · Zbl 0845.05043
[223] Korfhage, P. R., Forest-based σ-polynomials and hypergraph colorings, (Tech. Report 82-CSE-4 (1982), Dept. of Computer Sci. and Engineering, Southern Methodist Univ)
[224] Korfhage, P. R., Sigma polynomials for color-weighted graphs, I, (Tech. Report 82-CSE-13 (1982), Dept. of Computer Sci. and Engineering, Southern Methodist Univ)
[225] Korfhage, P. R., Sigma polynomials for color-weighted graphs, II, (Technical Report 82-CSE-14 (1982), Dept. of Computer Sci. and Engineering, Southern Methodist Univ)
[226] Korfhage, P. R., A note on quadratic σ-polynomials, Discrete Math., 69, 195-196 (1988), MR89f: 05084 · Zbl 0658.05026
[227] Kuksa, A. I., Discrete optimal selection problems, (Theory of Optimal Solutions Proc. Sem. Kiev. Theory of Optimal Solutions Proc. Sem. Kiev, 1968 (1968), Akad. Nauk Ukrain. SSR: Akad. Nauk Ukrain. SSR Kiev), 54-69, MR40: 1197
[228] Kung, J. P.S.; Murty, M. R.; Rota, G.-C., On the Redei zeta function, J. Number Theory, 12, 421-436 (1980), MR82c: 06018 · Zbl 0446.05003
[229] Lan, X. Q., On chromaticity of graphs, (Neimenggu Shida Xuebao Ziran Kexue Ban (1991)), 23-28, (Chinese, English summary). MR92j: 05071
[230] Las Vergnas, M., Sur les activités des orientations d’une géométrie combinatoire, Cahiers Centre Etudes Rech. Oper., 20, 293-300 (1978), MR81d: 05019 · Zbl 0404.05018
[231] Laskar, R.; Hare, W. R., The chromatic polynomial of a complete \(r\)-partite graph, Amer. Math. Monthly, 82, 752-754 (1975), MR53: 5355 · Zbl 0321.05110
[232] Lazebnik, F., On the greatest number of colorings of graphs with a fixed number of vertices and edges, (Congr. Number., 65 (1988)), 69-87, MR90j: 05068
[233] Lazebnik, F., On the greatest number of 2 and 3 colorings of a \((v, e)\)-graph, J. Graph Theory, 13, 203-214 (1989), MR90d: 05099 · Zbl 0677.05032
[234] Lazebnik, F., New upper bounds for the greatest number of proper colorings of a \((V, E)\)-graph, J. Graph Theory, 14, 25-29 (1990), MR91b: 05079 · Zbl 0688.05042
[235] Lazebnik, F., Some corollaries of a theorem of Whitney on the chromatic polynomial, Discrete Math., 87, 53-64 (1991), MR91m: 05084 · Zbl 0721.05021
[236] Eazuka, E., On chromaticity of graphs, Discuss. Math. Graph Theory, 15, 19-31 (1995), MR96c: 05060
[237] L.A. Lee, A note on chromatic equivalence, Preliminary Report A.M.S. Abstracts 711-05-22.; L.A. Lee, A note on chromatic equivalence, Preliminary Report A.M.S. Abstracts 711-05-22.
[238] Lee, L. A., On chromatically equivalent graphs, (Ph.D. Dissertation (1975), George Washington Univ) · Zbl 0483.05027
[239] Lehmer, D. H., The chromatic polynomial of a graph, Pacific J. Math., 118, 463-469 (1985), MR86g: 05035 · Zbl 0571.05019
[240] Lehmer, D. H., Coloring the Platonic solids, Amer. Math. Monthly, 93, 288-292 (1986), MR87e: 05072 · Zbl 0605.05011
[241] Lewis, D. C., A generalized Möbius inversion formula, Bull. Amer. Math. Soc., 78, 558-561 (1972), MR45: 8533 · Zbl 0254.05107
[242] Li, N. Z., On coefficients of σ-polynomials of graphs, J. Shanghai Sec. Polytechnic Univ., 1, 1-5 (1988)
[243] Li, N.-Z., The chromatic polynomials of disconnected unlabeled graphs, J. Shanghai Sec. Polytechnic Univ., 9, 14-21 (1992), (Chinese, English summary)
[244] Li, N. Z., On graphs having σ-polynomials of the same degree, Discrete Math., 110, 185-196 (1992), MR93k: 05065 · Zbl 0771.05038
[245] Li, N. Z.; Liu, R. Y., The chromaticity of the complete \(t\)-partite graph \(K(1, p_2\), …, \(p_t)\), J. Xinjiang Univ. Natur. Sci., 7, 95-96 (1990), MR91j: 05046 · Zbl 0964.05508
[246] Li, N. Z.; Sun, H. S.H.; Wen, I. X., Properties of chromatic polynomials of unlabeled graphs, J. Combin. Math. Combin. Comput., 17, 21-32 (1995), MR96b: 05062 · Zbl 0819.05028
[247] Li, N.-Z.; Whitehead, E. G., Classification of graphs having cubic σ-polynomials, (Graph Theory and Its Applications: East and West. Graph Theory and Its Applications: East and West, Ann. New York Acad. Sci., 576 (1989)), 328-335, MR92j: 05072 · Zbl 0793.05062
[248] Li, N.-Z.; Whitehead, E. G., The chromatic uniqueness of \(W_{10}\), Discrete Math., 104, 197-199 (1992), MR93e: 05034 · Zbl 0753.05035
[249] Li, N.-Z.; Whitehead, E. G., The chromaticity of certain graphs with five triangles, Discrete Math., 122, 365-372 (1993), MR94f: 05057 · Zbl 0787.05040
[250] Li, N.-Z.; Whitehead, E. G.; Xu, S.-J., Classification of chromatically unique graphs having quadratic σ-polynomials, J. Graph Theory, 11, 169-176 (1987), MR88c: 05057 · Zbl 0686.05021
[251] Li, W. M., Almost every \(K_4\)-homeormorph is chromatically unique, Ars Combin., 23, 13-35 (1987), MR88d: 05065
[252] Li, W. M., Some new results on chromatic uniqueness of \(K_4\) homeomorphs, Math. Appl., 4, 43-47 (1991), (Chinese, English summary). MR92k: 05049
[253] Li, W. X.; Tian, F., Some problems concerning the chromatic polynomials of graphs, Acta Math. Sinica, 21, 223-230 (1978), (Chinese, English summary). MR84i: 05049 · Zbl 0397.05026
[254] Lin, C. Q., Some recursive formulas for the chromatic polynomials of graphs, J. Math. (Wuhan), 7, 276-278 (1987), (Chinese). MR90a: 05086 · Zbl 0667.05026
[255] Lin, N.-W., Approximating the chromatic polynomial of a graph, (Graph-theoretic concepts in computer science. Graph-theoretic concepts in computer science, Lecture Notes in Comput. Sci., Vol. 790 (1994), Springer: Springer Berlin), 200-210, MR95d: 05054
[256] Lin, Y. X.; Zhang, F. J., Two short proofs on chromatic polynomials, Ars Combin., 27, 221-222 (1989), MR90f: 05061 · Zbl 0705.05035
[257] Linial, N., Legal coloring of graphs, Combinatorica, 6, 49-54 (1986), MR88a: 68055 · Zbl 0598.05035
[258] Lindstrom, B., Determinants on semilattices, (Proc. Amer. Math. Soc., 20 (1969)), 207-208, MR39: 102 · Zbl 0165.02902
[259] Liu, B. L.; Zhou, Z. H.; Tan, G. Q., The Akiyama-Harary problem for chromatic polynomials, Acta Math. Sci. (Chinese), 13, 252-255 (1993), (Chinese, Chinese summary). MR95d: 05055
[260] Liu, C. L., Introduction to Combinatorial Mathematics (1968), McGraw-Hill: McGraw-Hill New York, MR38: 3154 · Zbl 0188.03801
[261] Liu, C. L., Topics in Combinatorial Mathematics, Math. Assoc. Amer. (1972), MR49: 7145 · Zbl 0324.05001
[262] Liu, R. Y., On chromatic polynomials of graphs, ((1986), J. Qinghai Normal Univ), 22-26, (Chinese)
[263] Liu, R. Y., On chromatic polynomials of two classes of graphs, Kexue Tongbao, 32, 1147-1148 (1987)
[264] Liu, R. Y., A new method to find chromatic polynomial of graph and its applications, Kexue Tongbao, 32, 1508-1509 (1987)
[265] Liu, R. Y., On the note for chromatic polynomials, ((1987), J. Qinghai Normal Univ), 6-9, (Chinese, English summary)
[266] Liu, R. Y., Chromatic polynomials of complementary graphs of trees, J. Xinjiang Univ. Natur. Sci., 6, 6-8 (1989), (Chinese, English summary). MR91e: 05023 · Zbl 1056.05501
[267] Liu, R. Y., Adjoint polynomial of graphs, ((1990), J. Qinghai Normal Univ), 1-9, (Chinese, English summary)
[268] Liu, R. Y., Chromatic uniqueness of \(Kn − E(kPs ⌣ rPt)\), J. System Sci. Math. Sci., 12, 207-214 (1992), (Chinese, English summary). MR94b: 05084
[269] Liu, R. Y., Several results on adjoint polynomials of graphs, ((1992), J. Qinghai Normal Univ), 1-6, (Chinese, English)
[270] Liu, R. Y., The maximum number of proper 3-colorings of a graph, Math. Appl., 6, 88-91 (1993), (Chinese, English and Chinese summaries). MR94b: 05085
[271] Liu, R. Y., Chromatic uniqueness of complementary graph of \(P_{q−1}\), Pure Appl. Math. Suppl., 9, 2, 86-87 (1993)
[272] Liu, R. Y., On the irreducible graphs, J. Qinghai Normal Univ., No. 4, 29-33 (1993)
[273] Liu, R. Y., Chromatic uniqueness of complementary graph of \(P_{q−1}\), J. Math. Res. Exposition, 14, 469-475 (1994) · Zbl 0882.05066
[274] Liu, R. Y., Chromatic uniqueness of complements of union of irreducible cycles, Math. Appl., 7, 200-205 (1994), (Chinese, English and Chinese summaries). MR95h: 05068 · Zbl 0914.05028
[275] Liu, R. Y., Chromatic uniqueness of a kind of graph, J. Neimenggu Univ., 25, 469-475 (1994) · Zbl 1333.05118
[276] R.Y. Liu, Chromatic uniqueness of complementary graphs of a kind of trees, Math. Appl., to appear.; R.Y. Liu, Chromatic uniqueness of complementary graphs of a kind of trees, Math. Appl., to appear.
[277] R.Y. Liu, Adjoint polynomials and chromatically unique graphs, to appear.; R.Y. Liu, Adjoint polynomials and chromatically unique graphs, to appear. · Zbl 0878.05030
[278] Liu, R. Y.; Bao, X.-W., Chromatic uniqueness of the complements of 2-regular graphs, Pure Appl. Math. Suppl., 9, 2, 69-71 (1993)
[279] R.Y. Liu and Z.-Q. Chen, Two new classes of chromatically unique graphs, J. Neimenggu Univ., to appear.; R.Y. Liu and Z.-Q. Chen, Two new classes of chromatically unique graphs, J. Neimenggu Univ., to appear.
[280] Liu, R. Y.; Li, N. Z., Chromatic uniqueness of connected vertex-transitive graphs, Math. Appl., 4, 50-53 (1991), (Chinese, English summary). MR92f: 05048 · Zbl 0891.05033
[281] Liu, R. Y.; Li, N. Z., Chromatic uniqueness of a kind of graph of the \(K_n\) − \(E(G)\) type, Acta Math. Scientia, 14, 316-320 (1994) · Zbl 0900.05007
[282] R.Y. Liu and N.Z. Li, A family of chromatically unique graphs of the form \(K_nEG\); R.Y. Liu and N.Z. Li, A family of chromatically unique graphs of the form \(K_nEG\)
[283] Liu, R. Y.; Wang, J.-F., On chromatic uniqueness of complement of union of cycles and paths, Theoret. Comput. Sci., 1, 112-126 (1992), (Chinese, English summary)
[284] Loerinc, B., Chromatic uniqueness of the generalized θ-graphs, Discrete Math., 23, 313-316 (1978), MR80a: 05095 · Zbl 0389.05034
[285] Loerinc, B. M., Computing chromatic polynomials for special families of graphs, (Courant Computer Science Report # 19 (February 1980), New York University), 1980
[286] Loerinc, B.; Whitehead, E. G., Chromatic polynomials for regular graphs and modified wheels, J. Combin. Theory Ser. B, 31, 54-61 (1981), MR82k: 05048 · Zbl 0456.05029
[287] Lovász, L., Combinatorial Problems and Exercises (1979), North-Holland: North-Holland Amsterdam, MR80m: 05001 · Zbl 0439.05001
[288] Lunelli, M.; Ricci, G.; Bonecchi, M., Algoritmi combinatorici (1977), Franco Angeli Editore: Franco Angeli Editore Milan, MR58: 19332
[289] Mamedov, V. Kh., A combinatorial interpretation of chromatic polynomials, Izv. Akad. Nauk Azerbaǐdzan, SSR Ser. Fiz.-Tehn. Mat. Nauk, 2, 23-26 (1981), (Russian, Azerbaijani and English summaries). MR83c: 05058 · Zbl 0524.05035
[290] Mamedov, V. Kh., A chromatic polynomial and structure of graphs, Izv. Akad. Nauk Azerbaidẑan, SSR Ser. Fiz.-Tehn. Mat. Nauk, 2, 90-93 (1981), (Russian, Azerbaijani and English summaries). MR83e: 05053 · Zbl 0475.05032
[291] Mamedov, V. Kh., Chromatic equivalence of graphs, Math. Cybernet. Appl. Math., 31-34 (1981), MR84k: 05044a · Zbl 0666.05030
[292] Mamedov, V. Kh., Polynomials of graph colorings, Math. Cybernet. Appl. Math., 35-40 (1981), MR84k: 05044b · Zbl 0666.05029
[293] Mansfield, A. J.; Welsh, D. J.A., Some colouring problems and their complexity, Ann. Discrete Math., 13, 159-170 (1982), MR84a: 05028 · Zbl 0503.05027
[294] Margaglio, C., Un programa para el cambio de base de polinomios cromáticos, (Report No. 89-04 (1989), Dpto. de Mat. Puras y Aplicadas Univ. Simón Bolivar)
[295] Margaglio, C., Chromatic polynomials and classes of homeomorphic graphs, (Report No. 90-03 (1990), Dpto. de Mat. Puras y Aplicadas, Univ. Simón Bolivar)
[296] Martin, P., Anneau de Tutte-Grothendieck associé aux dénombrements, eulériennes dans les graphes 4-réguliers planaires, (Colloq. Théorie des Graphes. Colloq. Théorie des Graphes, Bruxelles, 1973. Colloq. Théorie des Graphes. Colloq. Théorie des Graphes, Bruxelles, 1973, Cahiers Centre Études Recherche Opér., 15 (1973)), 343-349, MR50: 1984 · Zbl 0268.05103
[297] Martin, P., Remarkable valuation of the dichromatic polynomial of planar multigraphs, J. Combin. Theory Ser. B, 24, 318-324 (1978), MR58: 335 · Zbl 0321.05108
[298] Matijasevich, Yu. V., A representation of the chromatic polynomial, Diskret. Anal., 31, 61-70 (1977), MR58: 27605 · Zbl 0435.05025
[299] McFall, J. D., Chromatic enumeration for triangulations, (Graph Theory and Related Topics (Proc. Conf. Univ. Waterloo, 1977) (1979), Academic Press: Academic Press New York), 305-314, MR81e: 05069 · Zbl 0466.05040
[300] Meredith, G. H.J., Coefficients of chromatic polynomials, J. Combin. Theory Ser. B, 13, 14-17 (1972), MR46: 8886 · Zbl 0218.05056
[301] Nagle, J. F., A new subgraph expansion for obtaining coloring polynomials for graphs, J. Combin. Theory Ser. B, 10, 42-59 (1971), MR44: 2663 · Zbl 0215.05505
[302] Nash-Williams, C. St. J.A., Possible directions in graph theory, (Combinatorial Mathematics and its Applications (Proc. Conf., Oxford 1969) (1971), Academic Press: Academic Press London), 191-200, MR44: 1593
[303] Negami, S., Polynomial invariants of graphs, Trans. Amer. Math. Soc., 299, 601-622 (1987), MR88a: 05129 · Zbl 0674.05062
[304] Nijenhuis, A.; Wilf, H. S., Combinatorial Algorithms (1975), Academic Press: Academic Press New York-London, MR53: 142 · Zbl 0298.05015
[305] Peng, Y. H., Three families of chromatically unique graphs, (Proc. Asian Math. Conf. (1990)), 357-362, MR93b: 00022 · Zbl 0940.05503
[306] Peng, Y. H., Chromatic uniqueness of certain \(K(2,4)\) homeomorphs, (Bahasa Malaysia), Matematika, 7, 101-111 (1991)
[307] Peng, Y. H., On the chromatic uniqueness of certain bipartite graphs, Discrete Math., 94, 129-140 (1991), MR92k: 05051 · Zbl 0752.05030
[308] Peng, Y. H., New infinite families of chromatically unique graphs, Sains Malaysiana (Quantitative Studies), 21, 15-25 (1992)
[309] Peng, Y. H., Three families of chromatically unique graphs, Serdica, 18, 10-16 (1992), MR93m: 05072 · Zbl 0808.05050
[310] Peng, Y. H., On the chromatic coefficients of a bipartite graph, Ars Combin., 34, 107-117 (1992), MR93i: 05064 · Zbl 0770.05047
[311] Peng, Y. H., On the chromatic uniqueness of certain trees of polygons, J. Austral. Math. Soc. Ser. A, 55, 1-8 (1993), MR94m: 05088 · Zbl 0795.05060
[312] Peng, Y. H., On the chromatic coefficients of a graph and chromatic uniqueness of certain \(n\)-partition graphs, (Combinatorics, Graph Theory, Algorithms and Applications (1993), World Sci. Publi: World Sci. Publi Beijing), 307-316, MR96b: 05064
[313] Peng, Y. H., Another family of chromatically unique graphs, Graphs Combin., 11, 285-291 (1995) · Zbl 0836.05028
[314] Peng, Y. H.; Little, C. H.C.; Teo, K. L.; Wang, H., Chromatic equivalence classes of certain generalized polygonal trees, (Report 38 (1994), Dept. of Math., Univer. Pertanian: Dept. of Math., Univer. Pertanian Malaysia) · Zbl 0883.05058
[315] Peng, Y. H.; Xu, S. J.; Liu, J. J., The chromaticity of \(s\)-bridge graphs and related graphs, Discrete Math., 135, 349-358 (1994) · Zbl 0814.05036
[316] Ray, N., Umbral calculus, binomial enumeration and chromatic polynomials, Trans. Amer. Math. Soc., 309, 191-213 (1988), MR89k: 05014 · Zbl 0666.05008
[317] Ray, N., Tutte algebras of graphs and formal group theory, (Proc. London Math. Soc., 65 (1992)), 23-45, MR93f: 05042 · Zbl 0773.05049
[318] Ray, N.; Schmitt, W., Coclosure operators and chromatic polynomials, (Proc. Nat. Acad. Sci. USA, 87 (1990)), 4685-4687, MR91j: 06006 · Zbl 0699.05027
[319] Ray, N.; Schmitt, W., Ultimate chromatic polynomials, Discrete Math., 125, 329-341 (1994) · Zbl 0796.05035
[320] Ray, N.; Schmitt, W.; Wright, C., Colouring simplicial complexes, Ars Combin., 29A, 161-169 (1990) · Zbl 0735.05040
[321] Ray, N.; Wright, C., Colourings and partition types: a generalized chromatic polynomial, Ars Combin., 25B, 277-286 (1988), MR89e: 05092 · Zbl 0662.05023
[322] Ray, N.; Wright, C., Umbral interpolation and the addition/contraction tree for graphs, Discrete Math., 103, 67-74 (1992), MR93g: 05054 · Zbl 0767.05015
[323] Read, R. C., Machine computation of the chromatic polynomials of graphs, with application to a cataloque of 7-node graphs, (Scientific Report UWI/CC8 (1967), Univ. of West Indices)
[324] Read, R. C., An introduction to chromatic polynomials, J. Combin. Theory, 4, 52-71 (1968), MR37: 104 · Zbl 0173.26203
[325] Read, R. C., Reviewer’s remarks (1975), MR50: 6906
[326] Read, R. C., Some applications of computers in graph theory, (Beineke, L. W.; Wilson, R. J., Selected Topics in Graph Theory (1978), Academic Press: Academic Press New York), 417-444, MR81e: 05059 · Zbl 0089.18301
[327] Read, R. C., Algorithms in graph theory, (Applications of Graph Theory (1979), Academic Press: Academic Press New York), 381-417, MR81h: 05050
[328] Read, R. C., A large family of chromatic polynomials, (Proc. Caribbean Conf. on Combin. and Computing (1981), Univ. of the West Indices: Univ. of the West Indices Barbados), 23-41, MR83e: 05054
[329] Read, R. C., Broken wheels are SLC, Ars Combin., 21A, 123-128 (1986), MR87f: 05074 · Zbl 0597.05033
[330] Read, R. C., An improved method for computing the chromatic polynomials of sparse graphs, (Research Report CORR 87-20 (1987), C & O Dept. Univ. of Waterloo)
[331] Read, R. C., Connectivity and chromatic uniqueness, Ars Combin., 23, 209-218 (1987), MR88c: 05058 · Zbl 0677.05055
[332] Read, R. C., On the chromatic properties of graphs up to 10 vertices, (Congr. Numer., 59 (1987)), 243-255, MR89d: 05077
[333] Read, R. C., A note on the chromatic uniqueness of \(W_{10}\), Discrete Math., 69, 317 (1988), MR89e: 05093 · Zbl 0639.05019
[334] Read, R. C., Recent advances in chromatic polynomial theory, (Proc. 5th Caribbean Conf. on Combin. and Comput.. Proc. 5th Caribbean Conf. on Combin. and Comput., Barbados (1988)) · Zbl 0677.05055
[335] Read, R. C.; Royle, G. F., Chromatic roots of families of graphs, (Graph Theory. Graph Theory, Combin. Appl. (1991)), 1009-1029, MR93b: 05003 · Zbl 0841.05034
[336] Read, R. C.; Tutte, W. T., Chromatic polynomials, (Beineke, L. W.; Wilson, R. J., Selected Topics in Graph Theory, Vol. 3 (1988), Academic Press: Academic Press New York), 15-42, MR93h: 05003 · Zbl 0667.05022
[337] Richmond, L. B.; Kasteleyn, P. W., Asymptotic behaviour of the coefficients of a chromatic sum, Ars Combin., 1, 253-259 (1976), MR54: 5032 · Zbl 0336.05109
[338] Robertson, I., \(T\)-chromatic polynomials, Discrete Math., 135, 279-286 (1994), MR95k: 05072 · Zbl 0814.05034
[339] Rota, G.-C., On the foundations of combinatorial theory, I. Theory of Möbius functions, Z. Wahr. Verw. Gebiete, 2, 340-368 (1964), MR30: 4688 · Zbl 0121.02406
[340] Saaty, T. L., Thirteen colorful variations on Guthrie’s four-color conjecture, Amer. Math. Monthly, 79, 2-43 (1972), MR45: 5026 · Zbl 0229.05110
[341] Saaty, T. L.; Kainen, P. C., The Four-Color Problem, Assauts and Conquest (1977), McGraw-Hill: McGraw-Hill New York, MR58: 246 · Zbl 0463.05041
[342] Sakaloglu, A.; Satyanarayana, A., Graphs with least number of colorings, J. Graph Theory, 19, 523-533 (1995) · Zbl 0830.05029
[343] Saleur, H., Zeros of chromatic polynomials: a new approach to Beraha conjecture using quantum groups, Comm. Math. Phys., 132, 657-679 (1990), MR91k: 17014 · Zbl 0708.05024
[344] P.M. Salzberg, Chromatic classification of \(K_pZZ\); P.M. Salzberg, Chromatic classification of \(K_pZZ\)
[345] Salzberg, P. M.; López, M. A.; Giudici, R. E., On the chromatic uniqueness of bipartite graphs, Discrete Math., 58, 285-294 (1986), MR87e: 05073 · Zbl 0594.05034
[346] Sands, D. A., Dichromatic polynomials of linear graphs, (Ph.D. Thesis (1972), Royal Holloway College: Royal Holloway College London)
[347] Sarti, S. D., Remarks on umbral evaluations of chromatic polynomials, Discrete Math., 126, 431-437 (1994) · Zbl 0795.05061
[348] Satyanarayana, S.; Tindell, R., Chromatic polynomials and network reliability, Discrete Math., 67, 57-79 (1987), MR88i: 05084 · Zbl 0647.05024
[349] Schwenk, A. J., On unimodal sequences of graphical invariants, J. Combin. Theory Ser. B, 30, 247-250 (1981), MR82h: 05036 · Zbl 0405.05051
[350] S.H. Scott, A method for finding the chromatic polynomial of a certain class of graphs, preprint.; S.H. Scott, A method for finding the chromatic polynomial of a certain class of graphs, preprint.
[351] Shier, D. R.; Chandrasekharan, N., Algorithms for computing the chromatic polynomial, J. Combin. Math. and Combin. Comput., 4, 213-222 (1988), MR90a: 05089 · Zbl 0665.05015
[352] Skupien, Z., Stirling number and colouring of \(q\)-trees, Scientific papers of the Institute of Mathematics of Wroclaw Technical University, Studies and Research, Vol. 13, 63-67 (1977), MR58: 5337
[353] Skupien, Z., Problem (on chromatic characterizations of \(q\)-trees), (Combinatorics I-II, Proc. Keszthely. Combinatorics I-II, Proc. Keszthely, 1976 (1978), North-Holland: North-Holland Amsterdam), 1212-1213
[354] Skupien, Z., Problem 2, Graphs, Hypergraphs and Matriods II, Zielona Góra 1987, (Proc. 6th Regional Scientific Session of Mathematicians held in Źagań (1987)), 97-98
[355] Smith, C. A.B., Map colourings and linear mappings, (Combinatorial Mathematics and its Applications. Combinatorial Mathematics and its Applications, Proc. Conf., Oxford 1969 (1971), Academic Press: Academic Press London), 259-283, MR43: 4722 · Zbl 0213.50703
[356] Smith, C. A.B., Electric currents in regular matroids, (Combinatorics (Proc. Conf. Combinatorial Math., Math. Inst. Oxford 1972) (1972), Inst. Math. Appl: Inst. Math. Appl Southend-on-Sea), 262-284, MR49: 7030
[357] Smith, C. A.B., On Tutte’s dichromatic polynomial, Ann. Discrete Math., 3, 247-257 (1978), MR58: 341 · Zbl 0381.05052
[358] Sobczyk, A.; Gettys, J. O., Extended chromatic polynomials, Canad. J. Math., 24, 492-501 (1972), MR45: 5027 · Zbl 0244.05105
[359] Sotskov, Ju. N.; Tanaev, V. S., Chromatic polynomial of a mixed graph, Vesci Akad. Navuk BSSR Ser. Fiz.-Mat. Navuk, No. 6, 20-23 (1976), MR57: 2972 · Zbl 0353.05037
[360] Stanley, R. P., A chromatic-like polynomial for ordered sets, (Proc. 2nd Chapel Hill Conf. on Combinatorial Mathematics and it Applications (1970), Univ. of North Carolina), 421-427, MR42: 4440
[361] Stanley, R. P., Acyclic orientations of graphs, Discrete Math., 5, 171-178 (1973), MR47: 6537 · Zbl 0258.05113
[362] Stanley, R. P., Combinatorial reciprocity theorems, Adv. Math., 14, 194-253 (1974), MR54: 111 · Zbl 0294.05006
[363] Stanley, R. P., A symmetric function generalization of the chromatic polynomial of a graph, Adv. Math., 111, 166-194 (1995), MR96b: 05174 · Zbl 0831.05027
[364] Swenson, J. R., The chromatic polynomial of a complete bipartite graph, Amer. Math. Monthly, 80, 797-798 (1973), MR48: 151 · Zbl 0271.05109
[365] Taylor, W., Generalized chromatic numbers, (Combinatorial Structures and their Applications (Proc. Calgary Internat. Conf., Calgary 1969) (1970), Gordon Breach: Gordon Breach New York), 421-422, MR42: 2981
[366] Teo, C. P.; Koh, K. M., The chromaticity of complete bipartite graphs with at most one edge deleted, J. Graph Theory, 14, 89-99 (1990), MR91g: 05050 · Zbl 0712.05027
[367] Teo, C. P.; Koh, K. M., The number of shortest cycles and the chromatic uniqueness of a graph, J. Graph Theory, 16, 7-15 (1992), MR93b: 05061 · Zbl 0770.05064
[368] Teo, C. P.; Koh, K. M., On chromatic uniqueness of uniform subdivisions of graphs, Discrete Math., 128, 327-335 (1994), MR95d: 05057 · Zbl 0796.05034
[369] Teo, K. L.; Koh, K. M., Chromatic classes of certain 2-connected \((n, n + 2)\)-graphs, Ars Combin., 32, 65-76 (1991), MR92j: 05076 · Zbl 0760.05044
[370] Thier, V., Graphen und Polynom (1983), Diploma. Tech. Univ. Munchen
[371] Thier, V.; Weickert, W., Ein Programm zur Berechnung und Analyse des chromatischen Polynoms (1981/1982), Fortgrschrittenenpraktikum für Informatiker an der Tech. Univ. München: Fortgrschrittenenpraktikum für Informatiker an der Tech. Univ. München WS
[372] C. Thomassen, On the number of Hamiton cycles in bipartite graphs, Combin. Prob. Comput., to appear.; C. Thomassen, On the number of Hamiton cycles in bipartite graphs, Combin. Prob. Comput., to appear. · Zbl 0868.05034
[373] C. Thomassen, The zero-free intervals for chromatic polynomials of graphs, Combin. Prob. Comput., to appear.; C. Thomassen, The zero-free intervals for chromatic polynomials of graphs, Combin. Prob. Comput., to appear. · Zbl 0887.05020
[374] Toft, B., A list of 25 graph colouring problems, (Graphen theorie und ihre Anwendungen (Stadt Wehlen, 1988). Graphen theorie und ihre Anwendungen (Stadt Wehlen, 1988), Dresdner Reihe Forsche., 9 (1988), Päd. Hochsch), 61-64, MR90c: 05096
[375] Toft, B., 75 graph-colouring problems, (Graph Colourings (1990), Longman Scientific & Technical: Longman Scientific & Technical New York), 9-35, MR93k: 05072 · Zbl 0693.05026
[376] Tomescu, I., Le nombre minimal de colorations d’un graphe, C.R. Acad. Sci. Paris Sér. A-B, 274, A539-A542 (1972), MR44: 6549
[377] Tomescu, I., On 3-colorings of bipartite \(p\)-threshold graphs, J. Graph Theory, 11, 327-338 (1987), MR88h: 05043 · Zbl 0662.05024
[378] Tomescu, I., Some extremal results concerning the number of graph and hypergraph colorings, (Proc. Combin. Graph Theory, Banach Center Publ., 25 (1989)), 187-194 · Zbl 0756.05058
[379] Tomescu, I., Maximal chromatic polynomials of connected planar graphs, J. Graph Theory, 14, 101-110 (1990), MR91g: 05051 · Zbl 0702.05033
[380] Tomescu, I., On the number of colorings of \(p\)-connected hypergraphs, (An. Univ. Bucuresti Mat., 39/40 (1990/1991), Matematică-Informatică), 98-101, MR94e: 05116
[381] Tomescu, I., On the sum of all distances in chromatic blocks, J. Graph Theory, 18, 83-102 (1994) · Zbl 0789.05036
[382] Tomescu, I., Maximum chromatic polynomials of 2-connected graphs, J. Graph Theory, 18, 329-336 (1994), MR95h: 05070 · Zbl 0809.05046
[383] Turan, P., On the theory of graphs, Colloq. Math., 3, 19-30 (1954), MR15: 976b · Zbl 0055.17004
[384] Tutte, W. T., A ring in graph theory, (Proc. Cambridge Philos. Soc., 43 (1947)), 26-40, MR8: 284k · Zbl 0031.41803
[385] Tutte, W. T., A contribution to the theory of chromatic polynomials, Canad. J. Math., 6, 80-91 (1954), MR15: 814c · Zbl 0055.17101
[386] Tutte, W. T., On dichromatic polynomials, J. Combin. Theory, 2, 301-320 (1967), MR36: 6320 · Zbl 0147.42902
[387] Tutte, W. T., More about chromatic polynomials and golden ratio, Combinatorial Structures and their Applications, (Combinatorial Structures and their Applications. Combinatorial Structures and their Applications, Proc. Calgary Internat. Conf., Calgary, Alta (1969), Gordon and Breach: Gordon and Breach New York), 439-453, MR41: 8299
[388] Tutte, W. T., Lectures on chromatic polynomials, (Institute of Statistics, Mimeo Series No. 600.25 (1970), University of North Carolina: University of North Carolina Chapel Hill) · Zbl 0209.55001
[389] Tutte, W. T., On chromatic polynomials and the golden ratio, J. Combin. Theory, 9, 289-296 (1970), MR42: 7557 · Zbl 0209.55001
[390] Tutte, W. T., The golden ratio in the theory of chromatic polynomials, Ann. New York Acad. Sci., 175, 391-402 (1970), MR42: 130 · Zbl 0227.05102
[391] Tutte, W. T., Dichromatic sums for rooted planar maps, (Combinatorics. Combinatorics, Proc. Symp. Pure Math., Vol. XIX (1971), Amer. Math. Soc: Amer. Math. Soc Providence), 235-245, MR47: 8350 · Zbl 0227.05103
[392] Tutte, W. T., The use of numerical computations in the enumerative theory of planar maps, (Proc. 25th Summer Meeting Canad. Math. Congress. Proc. 25th Summer Meeting Canad. Math. Congress, Lakehead Univ. 1971 (1971), Lakehead Univ), 2-40, MR50: 1965 · Zbl 0328.05116
[393] Tutte, W. T., Chromatic sums for rooted planar triangulations: the case \(λ = 1\) and \(λ = 2\), Canad. J. Math., 25, 426-447 (1973), MR47: 3228 · Zbl 0253.05122
[394] Tutte, W. T., Chromatic sums for rooted planar triangulations II: the case \(λ = τ + 1\), Canad. J. Math., 25, 657-671 (1973), MR50: 164 · Zbl 0268.05112
[395] Tutte, W. T., Chromatic sums for rooted planar triangulations III: the case \(λ = 3\), Canad. J. Math., 25, 780-790 (1973), MR50: 165 · Zbl 0268.05113
[396] Tutte, W. T., Chromatic sums for rooted planar triangulations IV: the case \(λ\) = ∞, Canad. J. Math., 25, 929-940 (1973), MR50: 166 · Zbl 0268.05114
[397] Tutte, W. T., Some polynomials associated with graphs, (Combinatories, Proc. British Combinatorial Conf. (1973)), 161-167, MR50: 4408 · Zbl 0299.05119
[398] Tutte, W. T., Chromatic sums for rooted planar triangulations V: special equations, Canad. J. Math., 26, 893-907 (1974), MR50: 167 · Zbl 0287.05103
[399] Tutte, W. T., (Chromials, Hypergraph Seminar. Chromials, Hypergraph Seminar, Lecture Notes in Math., Vol. 411 (1974), Springer: Springer Berlin), 243-266, MR51: 5370
[400] Tutte, W. T., Map-coloring problems and chromatic polynomials, Amer. Sci., 62, 702-705 (1974)
[401] Tutte, W. T., Codichromatic graphs, J. Combin. Theory Ser. B, 16, 168-174 (1974), MR48: 10876 · Zbl 0275.05108
[402] Tutte, W. T., The graph of the chromial of a graph, (Combinatorial Mathematics III. Combinatorial Mathematics III, Lecture Notes in Math., Vol. 452 (1975), Springer: Springer Berlin), 55-61, MR51: 10152 · Zbl 0311.05110
[403] Tutte, W. T., Chromials, (Studies in Graph Theory, Part II, Studies in Math., Vol. 12 (1975), Math. Assoc. Amer: Math. Assoc. Amer Washington, DC), 361-377, MR53: 10637 · Zbl 0297.05105
[404] Tutte, W. T., The dichromatic polynomial, (Congr. Numer. XV Utilitas Math. (1976)), 605-635, MR53: 186 · Zbl 0339.05105
[405] Tutte, W. T., Sommes chromatiques, Problémes combinatoires et théorie des graphes, (Colloq. Internat. CRNS. Colloq. Internat. CRNS, Univ. Orsay, Orsay, 1976. Colloq. Internat. CRNS. Colloq. Internat. CRNS, Univ. Orsay, Orsay, 1976, Colloques Internat. CNRS, 260 (1976), CRNS: CRNS Paris), 407-409, (English summary). MR80m: 05048
[406] Tutte, W. T., On a pair of functional equations of combinatorial interest, Aequationes Math., 17, 121-140 (1978), MR80h: 05026 · Zbl 0377.05025
[407] Tutte, W. T., All the king’s horses, (Graph Theory and Related Topics (1979), Academic Press: Academic Press New York), 15-33, MR81a: 05096 · Zbl 0472.05046
[408] Tutte, W. T., Rotors in graph theory, Ann. Discrete Math., 6, 343-347 (1980), MR83b: 05144 · Zbl 0484.05058
[409] Tutte, W. T., 1-factors and polynomials, Europ. J. Combin., 1, 77-87 (1980), MR81h: 05067 · Zbl 0439.05037
[410] Tutte, W. T., Chromatic solutions, Canad. J. Math., 34, 741-758 (1982), MR84b: 05049a · Zbl 0458.05010
[411] Tutte, W. T., Chromatic solutions, II, Canad. J. Math., 34, 952-960 (1982), MR84b: 05049b · Zbl 0505.05030
[412] Tutte, W. T., Counting rooted triangulations, (Theory and practice of combinatorics. Theory and practice of combinatorics, North-Holland Math. Stud., 60 (1982), North-Holland: North-Holland Amsterdam), 243-253, MR86j: 05079 · Zbl 0493.05032
[413] Tutte, W. T., Planar enumeration, (Graph Theory and Combinatorics (Cambridge 1983) (1984), Academic Press: Academic Press London), 315-319, MR86d: 05061 · Zbl 0547.05034
[414] Tutte, W. T., Map-colourings and differential equations, (Progress in Graph Theory (Waterloo, Ont., 1982) (1984), Academic Press: Academic Press New York), 477-485, MR86f: 05066 · Zbl 0554.05029
[415] Tutte, W. T., Graph Theory, (Encyclopedia of Mathematics and its Applications (1984), Addison-Wesley: Addison-Wesley Reading, MA), MR87c: 05001 · Zbl 0206.52603
[416] Tutte, W. T., On the Birkhoff-Lewis equation, Discrete Math., 92, 417-425 (1991), MR92k: 05052 · Zbl 0756.05059
[417] Tutte, W. T., The matrix of chromatic joins, J. Combin. Theory Ser. B, 57, 269-288 (1993), MR94a: 05144 · Zbl 0793.05030
[418] Tutte, W. T., The Birkhoff-Lewis equation for graph-colorings, Ann. Discrete Math., 55, 153-158 (1993), MR93k: 05003 · Zbl 0787.05042
[419] Vaderlind, P., Chromatic uniqueness of \(k\)-trees, (Report 1986 No. 9 (1986), Dept. of Math. University: Dept. of Math. University Stockholm)
[420] Vaderlind, P., Chromaticity of triangulated graphs, J. Graph Theory, 12, 245-248 (1988), MR89d: 05082 · Zbl 0666.05027
[421] Voloshin, V. I., Properties of triangulated graphs, (Issled. Oper. and Programming (Kishiniev) (1982)), 24-32, (Russian). MR85i: 05102 · Zbl 0502.05024
[422] Voloshin, V. I., Chromatic and dimensional polynomials of triangulated graphs, Matemat. Issled. (Kishiniev), 66, 24-29 (1982), (Russian). MR83e: 05056 · Zbl 0502.05024
[423] Voloshin, V. I., A conditional chromatic polynomial, Studies Appl. Math. Inform. Sci. “Shtiintsa”, Kshiner, 192, 16-19 (1990), (Russian). MR91h: 05055
[424] Voloshin, V. I., A note on the conditional chromatic polynomial, Glasgow Math. J., 36, 265-267 (1994), MR95g: 05049 · Zbl 0810.05024
[425] Voloshin, V. I.; Gorgos, I. M., Some properties of weakly connected hypergraphs and their applications, Maternat. Issled. (Kishiniev), 66, 30-33 (1982), MR83m: 05093 · Zbl 0501.05047
[426] S.A. Wahid, A representation of the chromatic polynomial as the determinant of a matrix, Research Report No. 05-01-88, Univ. of the West Indices, Trinidad.; S.A. Wahid, A representation of the chromatic polynomial as the determinant of a matrix, Research Report No. 05-01-88, Univ. of the West Indices, Trinidad. · Zbl 1023.05116
[427] Wakelin, C. D., The chromatic polynomial relative to the complete graph basis, manuscript (1993)
[428] Wakelin, C. D.; Woodall, D. R., Chromatic polynomials, polygon trees, and outerplanar graphs, J. Graph Theory, 16, 459-466 (1992), MR93k: 05067 · Zbl 0778.05074
[429] Wanner, T., On the chromaticity of certain subgraphs of a \(q\)-tree, J. Graph Theory, 13, 597-605 (1989), MR90j: 05057 · Zbl 0698.05029
[430] W. Weickert, Untersuchungen zum chromatischen Polynom anhand spezieller Basisdarstellungen, Diploma Thesis, Tech Univ. Munchen.; W. Weickert, Untersuchungen zum chromatischen Polynom anhand spezieller Basisdarstellungen, Diploma Thesis, Tech Univ. Munchen.
[431] Welsh, D. J.A., Colourings, flows and projective geometry, Nieuw Arch. Wisk., 28, 3, 159-176 (1980), MR82h: 05002 · Zbl 0452.05015
[432] Wentzlau, M., Problem 4, Graphs, Hypergraphs and Matriods II, Zielona Góra 1987, (Proc. 6th Regional Scientific Session of Mathematicians. Proc. 6th Regional Scientific Session of Mathematicians, Źagań (1987)), 99-100
[433] Whitehead, E. G., Chromatic polynomials for chorded cycles, (Proc. 6th SEA Conf. on Combinatorics. Proc. 6th SEA Conf. on Combinatorics, Graph Theory and Computing, Utilitas Math. (1975)), 619-625, MR52: 13467
[434] Whitehead, E. G., Stirling number identities from chromatic polynomials, J. Combin. Theory Ser. A, 24, 314-317 (1978), MR58: 269 · Zbl 0383.05016
[435] Whitehead, E. G., Chromaticity of two-trees, J. Graph Theory, 9, 279-284 (1985), MR86i: 05065 · Zbl 0574.05016
[436] Whitehead, E. G., Chromatic polynomials of generalized trees, Discrete Math., 72, 391-393 (1988), MR89m: 05052 · Zbl 0659.05045
[437] Whitehead, E. G., Chromatic polynomials and the structure of graphs, (Graph Theory and its Applications: East and West. Graph Theory and its Applications: East and West, Ann. New York Acad. Sci., 576 (1989)), 630-632, MR92f: 05041 · Zbl 0792.05059
[438] E.G. Whitehead Jr., Chromaticity of \(K_4\); E.G. Whitehead Jr., Chromaticity of \(K_4\)
[439] Whitehead, E. G.; Zhao, L.-C., Chromatic uniqueness and equivalence of \(K_4\) homeomorphs, J. Graph Theory, 8, 355-364 (1984), MR85g: 05078 · Zbl 0555.05035
[440] Whitehead, E. G.; Zhao, L.-C., Cutpoints and the chromatic polynomial, J. Graph Theory, 8, 371-377 (1984), MR85i: 05111 · Zbl 0551.05041
[441] Whitney, H., The coloring of graphs, Ann. Math., 33, 12, 688-718 (1932) · JFM 58.0606.01
[442] Whitney, H., A logical expansion in mathematics, Bull. Amer. Math. Soc., 38, 572-579 (1932) · JFM 58.0605.08
[443] Wilf, H. S., Hadamard determinants, Möbius functions, and the chromatic number of a graph, Bull. Amer. Math. Soc., 74, 960-964 (1968), MR37: 5106 · Zbl 0172.01602
[444] Wilf, H. S., The Möbius function in combinatorial analysis and chromatic graph theory, (Proof Techniques in Graph Theory (1969), Academic Press: Academic Press New York), 179-188, MR40: 7126 · Zbl 0205.28403
[445] Wilf, H. S., An analogue of the chromatic polynomial for the vertex assignments modulo 3, Combinatorial Mathematics and its Applications, (Proc. Conf.. Proc. Conf., Oxford (1971), Academic Press: Academic Press New York), 311-313, MR43: 3168
[446] Wilf, H. S., Which polynomials are chromatic?, (International Colloquium on Theoretical Combinatorics (Sept. 1973), Amer. Math. Soc: Amer. Math. Soc Rome), MR56: 11841 · Zbl 0205.28403
[447] Wilf, H. S., A note on
((P\)(−λ; G)\), J. Combin. Theory Ser. B, 22, 296 (1977), MR56: 11842 · Zbl 0369.05030
[448] Wilson, R. J., The Möbius function in combinatorial mathematics, (Combinatorial Mathematics and its Applications Proc. Conf.. Combinatorial Mathematics and its Applications Proc. Conf., Oxford 1969 (1971), Academic Press: Academic Press London), 315-333, MR43: 3136
[449] Woodall, D. R., Zeros of chromatic polynomials, (Cameron, P. J., Combinatorial Survey, Proc. 6th British Combinat. Conf. (1977), Academic Press: Academic Press London), 199-223, MR57: 2974 · Zbl 0357.05044
[450] Woodall, D. R., An inequality for chromatic polynomials, Discrete Math., 101, 327-331 (1992), MR93k: 05070 · Zbl 0762.05010
[451] Woodall, D. R., A zero-free interval for chromatic polynomials, Discrete Math., 101, 333-341 (1992), MR93k: 05071 · Zbl 0766.05030
[452] Wumaier, A., The chromatic polynomials of a class of graphs, J. Xinjiang Univ. Natur. Sci., 5, 109-110 (1988), (Chinese). MR90f: 05062
[453] Xu, J.; Li, H., Chromatic polynomials of connection \(n\)-cycle graphs, J. Northwest Univ., 22, 147-152 (1992)
[454] Xu, J.; Li, H., A new method of calculating chromatic polynomials: a recursive algorithm using vertex contraction, J. Northwest Univ., 24, 103-105 (1994), (Chinese, English and Chinese summaries)
[455] Xu, S.-J., Complete-graph-basis and the chromaticity of graphs with more edges, J. Shanghai Teachers College, 3, 18-23 (1983) · Zbl 0597.05031
[456] Xu, S.-J., The chromaticity of regular graphs and bigraphs with more edges, J. Shanghai Teachers College, 1, 10-18 (1984) · Zbl 0597.05032
[457] Xu, S.-J., Some notes on chromatic uniqueness of graphs, J. Shanghai Teach. Univ., Nat. Sci. Ed., 2, 10-12 (1987), (Chinese, English summary) · Zbl 0636.05027
[458] Xu, S.-J., On σ-polynomials, Discrete Math., 69, 189-194 (1988), MR89f: 05083 · Zbl 0658.05025
[459] Xu, S., The chromatic uniqueness of complete bipartite graphs, Discrete Math., 94, 153-159 (1991), MR92h: 05059 · Zbl 0752.05031
[460] Xu, S., A lemma in studying chromaticity, Ars Combin., 32, 315-318 (1991), MR92m: 05088 · Zbl 0753.05039
[461] Xu, S., Corrigendum, Discrete Math., 104, 217 (1992) · Zbl 0760.05046
[462] Xu, S., Chromaticity of a family of \(K_4\)-homeomorphs, Discrete Math., 117, 293-297 (1993), MR94b: 05090 · Zbl 0781.05022
[463] Xu, S., Classes of chromatically equivalent graphs and polygon trees, Discrete Math., 133, 267-278 (1994), MR95i: 05062 · Zbl 0813.05030
[464] Xu, S.-J.; Li, N.-Z., The chromaticity of wheels, Discrete Math., 51, 207-212 (1984), MR85i: 05112 · Zbl 0547.05032
[465] Xu, S.-J.; Liu, J. J.; Peng, Y. H., The chromaticity of \(s\)-bridge graphs and related graphs, Discrete Math., 135, 349-358 (1994) · Zbl 0814.05036
[466] Ye, C.-F.; Liu, R. Y., Chromatic uniqueness of a new family of graphs, Pure Appl. Math., 10, 46-53 (1994), (Special Issue)
[467] Yueh, K.; Bedrosian, S. D., Coefficient relationship between rook and chromatic polynomials, J. Franklin Inst., 302, 313-317 (1976), MR55: 10311 · Zbl 0352.05032
[468] Zaslavsky, T., Biased graphs, III, chromatic and dichromatic invariants, J. Combin. Theory Ser. A, 64, 17-88 (1995) · Zbl 0857.05088
[469] Zhang, J. G.; Xue, T., Chromaticity of complete bipartite graphs, J. System Sci. Math. Sci., 11, 381-383 (1991), MR92i: 05100 · Zbl 0747.05040
[470] D. Zeitlin, A polynomial identity for the chromatic polynomial of a complete \(r\); D. Zeitlin, A polynomial identity for the chromatic polynomial of a complete \(r\)
[471] Zykov, A. A., Math. Sb., 24, 163-188 (1949), MR11: 733h
[472] Zykov, A. A., Cyclomatic and distribution properties of multigraphs, Doklady Akad. Nauk SSSR, 143, 1264-1267 (1962), MR27: 1933 · Zbl 0117.17202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.