A note on randomly colored matchings in random bipartite graphs

We are given a bipartite graph that contains at least one perfect matching and where each edge is colored from a set Q=\{c_1,c_2,\ldots,c_q}\. Let $Q_i=\set{e\in E(G):c(e)=c_i}$, where $c(e)$ denotes the color of $e$. The perfect matching color profile $mcp(G)$ is defined to be the set of vectors $(m_1,m_2,\ldots,m_q)\in [n]^q$ such that there exists a perfect matching $M$ such that $|M\cap Q_i|=m_i$. We give bounds on the matching color profile for a randomly colored random bipartite graph.