Suppose we have two bipartite graphs $G_1$ and $G_2$ with perfect matching count $P_1$ and $P_2$ respectively then their disjoint union gives a bipartite graph with perfect matching $P_1P_2$.
Is there a graph construction from $G_1$ to get a bipartite graph with perfect matching count $P_1+1$ in polynomial time without knowing $P_1$?
