2 problems

Let $G\sim G(n,n,p)$ be a random bipartite graph with two parts of size $n$, and let $\operatorname{tc}_3(G)$ be the minimum number of monochromatic trees whose vertices cover $G$…

Let $K_{n,m}$ be the complete bipartite graph with parts of sizes $n$ and $m$, and let $\operatorname{tc}_r(K_{n,m})$ be the minimum number of monochromatic trees whose vertices co…