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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

Provided by:
arXiv.org e-Print Archive

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