An improved bound on the sizes of matchings guaranteeing a rainbow matching
Combinatorics
2015-03-03 v1
Abstract
A conjecture by Aharoni and Berger states that every family of matchings of size in a bipartite multigraph contains a rainbow matching of size . In this paper we prove that matching sizes of suffice to guarantee such a rainbow matching, which is asymptotically the same bound as the best known one in case we only aim to find a rainbow matching of size . This improves previous results by Aharoni, Charbit and Howard, and Kotlar and Ziv.
Keywords
Cite
@article{arxiv.1503.00438,
title = {An improved bound on the sizes of matchings guaranteeing a rainbow matching},
author = {Dennis Clemens and Julia Ehrenmüller},
journal= {arXiv preprint arXiv:1503.00438},
year = {2015}
}