Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On fundamental transversal matroids

Author: R. A. Brualdi
Journal: Proc. Amer. Math. Soc. 45 (1974), 151-156
MSC: Primary 05B35
MathSciNet review: 0387087
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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 44 #3899. MR 0286690 (44:3899)
  • [2] H. Crapo and G. C. Rota, On the foundations of combinatorial theory: Combinatorial geometries, Preliminary edition, M. I.T. Press, Cambridge, Mass., 1970. MR 45 #74. MR 0290980 (45:74)
  • [3] J. Edmonds and D. R. Fulkerson, Transversals and matroid partition, J. Res. Nat. Bur. Standards Sect. B 69 B (1965), 147-153. MR 32 #5531. MR 0188090 (32:5531)
  • [4] F. Harary and D. 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 41 #8267. MR 0263666 (41:8267)
  • [5] M. 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. MR 42 #1663. MR 0266760 (42:1663)
  • [6] L. Mirsky, Transversal theory. An account of some aspects of combinatorial mathematics, Math. in Science and Engineering, vol. 75, Academic Press, New York, 1971. MR 44 #87. MR 0282853 (44:87)
  • [7] H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57 (1935), 509-553. MR 1507091

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05B35

Retrieve articles in all journals with MSC: 05B35

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society