A Tverberg type theorem for matroids
Combinatorics
2016-11-29 v2
Abstract
Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d+1, then for any continuous map f from the matroidal complex M into the d-dimensional Euclidean space there exist t \geq \sqrt{b(M)}/4 disjoint independent sets \sigma_1,\ldots,\sigma_t \in M such that \bigcap_{i=1}^t f(\sigma_i) \neq \emptyset.
Cite
@article{arxiv.1607.01599,
title = {A Tverberg type theorem for matroids},
author = {Imre Bárány and Gil Kalai and Roy Meshulam},
journal= {arXiv preprint arXiv:1607.01599},
year = {2016}
}
Comments
This article is due to be published in the collection of papers "A Journey through Discrete Mathematics. A Tribute to Jiri Matousek" edited by Martin Loebl, Jaroslav Nesetril and Robin Thomas, due to be published by Springer