Rainbow Matchings: existence and counting
Combinatorics
2011-04-15 v1 Discrete Mathematics
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.
Cite
@article{arxiv.1104.2702,
title = {Rainbow Matchings: existence and counting},
author = {Guillem Perarnau and Oriol Serra},
journal= {arXiv preprint arXiv:1104.2702},
year = {2011}
}
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12 pages