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 $B_{n,p}$ denote the random bipartite graph with edge-probability parameter $p$, and let $\chi_g(B_{n,p})$ denote its game chromatic number. Random bipartite graph game chromat…