2011/04/14 by Guillem Perarnau, Perarnau, Guillem, Oriol Serra +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1104.2702
12 pages
arxiv created 2011/04/14 · arxiv updated 2011/04/15
A perfect matching M in an edge-colored complete bipartite graph Kn,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 Kn,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.