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Matroid basis graphs. I. (English) Zbl 0244.05015

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
05C99 Graph theory
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[1] Bondy, J. A.: Pancyclic graphs. II, university of Waterloo. Proceedings of the second louisiana conference on combinatorics, graph theory and computing (1971) · Zbl 0291.05109
[2] Crapo, H. H.; Rota, G. -C: On the foundations of combinatorial theory: combinatorial geometries. (1970) · Zbl 0216.02101
[3] Cummins, R. L.: Hamiltonian circuits in tree graphs. IEEE trans. Circuit theory 13, 82-90 (1966)
[4] Cunningham, W.: The basis graph of a matroid. (1972) · Zbl 0247.20055
[5] Gewirtz, A.: Graphs with maximal even girth. Canad. J. Math. 21, 915-934 (1969) · Zbl 0181.51801
[6] Harary, F.: Graph theory. (1969) · Zbl 0182.57702
[7] Holzmann, C. A.; Harary, F.: On the tree graph of a matroid. SIAM J. Appl. math. 22, 187-193 (1972) · Zbl 0249.05102
[8] C. A. Holzmann, P. G. Norton, and M. D. Tobey, A graphical representation of matroids, to appear in Siam J. Appl. Math. · Zbl 0241.05020
[9] Kishi, G.; Kajitani, Y.: On the realization of tree graphs. IEEE trans. Circuit theory 15, 271-273 (1968)
[10] Maurer, S. B.: Matroid basis graphs. Ph.d. dissertation (May, 1972) · Zbl 0247.05018
[11] S. B. Maurer, Matroid basis graphs. II, to appear in J. Combinatorial Theory, Ser. B.
[12] Piff, M. J.; Welsh, D. J. A: On the number of combinatorial geometries. Bull. London math. Soc. 3, 55-56 (1971) · Zbl 0222.05003
[13] Shank, H.: A note on Hamiltonian circuits in tree graphs. IEEE trans. Circuit theory 15, 86 (1968) · Zbl 0164.05201
[14] Tutte, W. T.: A homotopy theorem for matroids. I–II. Trans. amer. Math. soc. 88, 144-174 (1958) · Zbl 0081.17301
[15] Tutte, W. T.: Lectures on matroids. J. res. Nat. bur. Standards, sect. B 69, 1-48 (1965) · Zbl 0151.33801
[16] Whitney, H.: The abstract properties of linear independence. Amer. J. Math. 57, 509-533 (1935) · Zbl 0012.00404
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