On fundamental transversal matroids

Brualdi, R. A.

doi:10.1090/S0002-9939-1974-0387087-4

On fundamental transversal matroids
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by R. A. Brualdi

Proc. Amer. Math. Soc. 45 (1974), 151-156

DOI: https://doi.org/10.1090/S0002-9939-1974-0387087-4

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Abstract:

Unified proofs of two theorems on fundamental transversal matroids are presented. A necessary condition for a matroid to be a fundamental transversal matroid with respect to a given basis is given.

References

J. A. Bondy and D. J. A. Welsh, Some results on transversal matroids and constructions for identically self-dual matroids, Quart. J. Math. Oxford Ser. (2) 22 (1971), 435–451. MR 286690, DOI 10.1093/qmath/22.3.435
Henry H. Crapo and Gian-Carlo Rota, On the foundations of combinatorial theory: Combinatorial geometries, Preliminary edition, The M.I.T. Press, Cambridge, Mass.-London, 1970. MR 0290980
Jack Edmonds and D. R. Fulkerson, Transversals and matroid partition, J. Res. Nat. Bur. Standards Sect. B 69B (1965), 147–153. MR 188090
Frank Harary and Dominic Welsh, Matroids versus graphs, The Many Facets of Graph Theory (Proc. Conf., Western Mich. Univ., Kalamazoo, Mich., 1968) Springer, Berlin, 1969, pp. 155–170. MR 0263666
Michel Las Vergnas, Sur les systèmes de représentants distincts d’une famille d’ensembles, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A501–A503 (French). MR 266760
L. Mirsky, Transversal theory. An account of some aspects of combinatorial mathematics, Mathematics in Science and Engineering, Vol. 75, Academic Press, New York-London, 1971. MR 0282853
Hassler Whitney, On the Abstract Properties of Linear Dependence, Amer. J. Math. 57 (1935), no. 3, 509–533. MR 1507091, DOI 10.2307/2371182