An improved bound on the sizes of matchings guaranteeing a rainbow matching

Autor:	Clemens, Dennis, Ehrenmüller, Julia
Rok vydání:	2015
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	A conjecture by Aharoni and Berger states that every family of $n$ matchings of size $n+1$ in a bipartite multigraph contains a rainbow matching of size $n$. In this paper we prove that matching sizes of $(3/2 + o(1)) n$ 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 $n-1$. This improves previous results by Aharoni, Charbit and Howard, and Kotlar and Ziv.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1503.00438 Zobrazit plný text záznamu View this record from Arxiv