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.
Connections
Explore this paper’s authors, topics and related work.
Building this map preview
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Reviews 0
Write a review
No reviews yet.
Discussion 0
Add a comment
No comments yet.