A combinatorial version of the colorful Caratheodory theorem
Combinatorics
2013-09-03 v3
Abstract
We give the following extension of Barany's colorful Caratheodory theorem: Let M be an oriented matroid and N a matroid with rank function r, both defined on the same ground set V and satisfying rank(M) < rank(N). If every subset A of V with r(V - A) < rank (M) contains a positive circuit of M, then some independent set of N contains a positive circuit of M.
Keywords
Cite
@article{arxiv.1305.3960,
title = {A combinatorial version of the colorful Caratheodory theorem},
author = {Andreas Holmsen},
journal= {arXiv preprint arXiv:1305.3960},
year = {2013}
}