2 problems

Let $\mathcal{B}(n_0,n_1)$ be the class of all bipartite graphs with bipartition $P_0$ and $P_1$, where $|P_i|=n_i$ for $i\in\{0,1\}$. Let $H(v,n_0,n_1)$ denote the rooted depth-…

Let $H(u;n_0,n_1)$ be the rooted depth-$2$ bipartite tree with bipartition $(A_0,A_1)$, where $|A_i|=n_i$ for $i\in\{0,1\}$, the root $u\in A_0$ is adjacent to every vertex of…