Title: An improved bound on the sizes of matchings guaranteeing a rainbow matching
Language: English
Authors: Clemens, Dennis  
Ehrenmüller, Julia 
Keywords: Bipartite graphs; Rainbow matchings
Issue Date: 15-Apr-2016
Source: Electronic Journal of Combinatorics 2 (23): P2.11 (2016-04-15)
Abstract (english): 
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 the case where 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.
URI: http://hdl.handle.net/11420/5949
ISSN: 2156-3527
Journal: The journal of combinatorics 
Institute: Mathematik E-10 
Document Type: Article
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