A theorem of the transversal theory for matroids of finite character

Abstract

This result was tit proved by P. Hall [3] for condition (a) and later by M. Hall Jr. [Z] for condition (b), and SO the result is conveniently referred to as Hall’s theonem. Brualdi and Scrimger [1] (using properties of matroids) extended Theorem 1.1 by g&g necessary and sufficient conditions for the existexe of a transversal of a system having an arbitrary number of finite sets and a k&e number of infinite sets, Wodd [S] proved an equivalent result (Theorem 1.2 below) using a simpler, more direct argument. In this note we generalize this result by giving necessary and sufficient conditions for such systems to have a transversal which is ak indkpendent set in some independence structure.

DOI: 10.1016/0012-365X(78)90005-5

Cite this paper

@article{Gyri1978ATO, title={A theorem of the transversal theory for matroids of finite character}, author={Ervin Gy{\"{o}ri and Eric C. Milner}, journal={Discrete Mathematics}, year={1978}, volume={23}, pages={235-240} }