A note on randomly colored matchings in random bipartite graphs
Abstract
We are given a bipartite graph that contains at least one perfect matching and where each edge is colored from a set Q=\c1,c2,…,cq\. Let Qi=e∈ E(G):c(e)=ci, where c(e) denotes the color of e. The perfect matching color profile mcp(G) is defined to be the set of vectors (m1,m2,…,mq)∈ [n]q such that there exists a perfect matching M such that |M Qi|=mi. We give bounds on the matching color profile for a randomly colored random bipartite graph.
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