Abstract
A fundamental transversal matroid (f.t.m.) is a transversal matroid which arises from the family of cocircuits with respect to a cobase. A characterization of binary f.t.m.'s is given in the form of excluded minor type. It is also shown that a binary f.t.m. is a special sort of series-parallel graphs.
Similar content being viewed by others
References
Bondy, J.A.: Transversal matroids, base orderable matroids, and graphs. Q. J. Math., Oxford (2)23, 81–89 (1972)
Bondy, J.A., Welsh, D.J.A.: Some results on transversal matroids and constructions for identically self-dual matroids. Q. J. Math., Oxford (2)22, 435–451 (1971)
Bulaldi, R.A.: On fundamental transversal matroids. Proc. Amer. Math. Soc.45, 151–156 (1974)
Brylawski, T.H.: An affine representation for transversal geometries. Stud. Appl. Math.54, 143–160 (1975)
Edmonds, J., Fulkerson, D.R.: Transversals and matroid partition. J. Res. Natl. Bur. Stand. Sct.B 69, 147–153 (1965)
Las Vergnas, M.: Sur les systèmes de représents distincts d'une famille d'ensembles. C. R. Acad. Sci., Paris,270, 501–503 (1970)
Sousa, J.D., Welsh, D.J.A.: A characterisation of binary transversal structures. J. Math. Anal. Appl.40, 55–59 (1972)
Welsh, D.J.A.: Matroid Theory. London: Academic Press 1976
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nakamura, M. A note on binary fundamental transversal matroids. Graphs and Combinatorics 5, 371–372 (1989). https://doi.org/10.1007/BF01788693
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01788693