Skip to main content
Article thumbnail
Location of Repository

Rainbow Matchings: existence and counting

By Guillem Perarnau and Oriol Serra

Abstract

A perfect matching M in an edge-colored complete bipartite graph K_{n,n} is rainbow if no pair of edges in M have the same color. We obtain asymptotic enumeration results for the number of rainbow matchings in terms of the maximum number of occurrences of a color. We also consider two natural models of random edge-colored K_{n,n} and show that, if the number of colors is at least n, then there is with high probability a random matching. This in particular shows that almost every square matrix of order n in which every entry appears at most n times has a Latin transversal.Comment: 12 page

Topics: Mathematics - Combinatorics, Computer Science - Discrete Mathematics
Year: 2011
OAI identifier: oai:arXiv.org:1104.2702
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://arxiv.org/abs/1104.2702 (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.