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Vertices missed by longest paths or circuits. (English) Zbl 0259.05120

MSC:
05C35 Extremal problems in graph theory
05C10 Planar graphs; geometric and topological aspects of graph theory
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[1] Berge, C.: Problèmes plaisants et delectables, no. 29. Rev. franç. Rech. opérat. 7, 405-406 (1963)
[2] Berge, C.: Graphes et hypergraphes. (1970) · Zbl 0213.25702
[3] Bilinski, S.; Blanuša, D.: Proof of the indecomposability of a certain graph. Hrvatsko prirodoslovno društvo. Glasnik mat.-fiz. Astr. ser. II 4, 78-80 (1949)
[4] Bondy, J. A.: Variations on the Hamiltonian theme. Canad. math. Bull. 15, 57-62 (1972) · Zbl 0238.05115
[5] Busacker, R. G.; Saaty, T. L.: Finite graphs and networks. (1965) · Zbl 0146.20104
[6] Chen, W. -K: Applied graph theory. (1971) · Zbl 0229.05107
[7] Chvátal, V.: Flip-flops in hypohamiltonian graphs. Canad. math. Bull. 16, 33-41 (1973) · Zbl 0253.05142
[8] Chvátal, V.: New directions in Hamiltonian graph theory. New directions in the theory of graphs, 65-95 (1973)
[9] Erdös, P.; Katona, G.: Theory of graphs. Proc. colloq. Tihany (1968) · Zbl 0155.00201
[10] Faulkner, G. B.: Recursive generation of cyclically k-connected cubic planar graphs. Ph.d. thesis (1971) · Zbl 0327.05114
[11] Faulkner, G. B.; Younger, D. H.: Non-Hamiltonian cubic planar maps. Discrete math. 7, 67-74 (1974) · Zbl 0271.05106
[12] Grinberg, E. J.: Plane homogeneous graphs of degree three without Hamiltonian circuits. Latvian math. Yearbook 4, 51-58 (1968) · Zbl 0185.27901
[13] Grünbaum, B.: Polytopes, graphs, and complexes. Bull. amer. Math. soc. 76, 1131-1201 (1970) · Zbl 0211.25001
[14] Herz, J. C.; Duby, J. J.; Vigué, F.: Recherche systématique des graphes hypohamiltoniens. Théorie des graphes, 153-160 (1967) · Zbl 0196.56102
[15] Herz, J. C.; Gaudin, T.; Rossi, P.: Solution du problème no. 29. Rev. franç. Rech. opérat. 8, 214-218 (1964)
[16] J. D. Horton, A hypotraceable graph (to appear).
[17] Kapoor, S. F.; Kronk, H. V.; Lick, D. R.: On detours in graphs. Canad. math. Bull. 11, 195-201 (1968) · Zbl 0167.22002
[18] Kronk, H. V.: Does there exist a hypotraceable graph?. Amer. math. Monthly 76, 809-810 (1969)
[19] Lindgren, W. F.: An infinite class of hypohamiltonian graphs. Amer. math. Monthly 74, 1087-1089 (1967) · Zbl 0158.42503
[20] Sachs, H.: Ein von kozyrev und grinberg angegebener nicht-hamiltonischer kubischer planarer graph. Beiträge zur graphentheorie, 127-130 (1968) · Zbl 0169.26402
[21] Thomassen, C.: Hypohamiltonian and hypotraceable graphs. Aarhus univ. Mat. inst. Preprint series, No. No. 61 (1972–1973) · Zbl 0272.05114
[22] Tutte, W. T.: A theorem on planar graphs. Trans. amer. Math. soc. 82, 99-116 (1956) · Zbl 0070.18403
[23] Walther, H.: Über die nichtexistenz eines knotenpunktes, durch den alle längsten wege eines graphes gehen. J. combinatorial theory 6, 1-6 (1969) · Zbl 0184.27504
[24] Walther, H.: Über die nichtexistenz zweier knotenpunkte eines graphen, die alle längsten kreise fassen. J. combinatorial theory 8, 330-333 (1970) · Zbl 0191.55203
[25] Zamfirescu, T.: A two-connected planar graph without concurrent longest paths. J. combinatorial theory sect. B 13, 116-121 (1972) · Zbl 0243.05110
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