All Questions

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 ...

According to a conjecture: Conjecture (Fan & Raspaud, 1994) Every bridgeless cubic graph contains three perfect matchings with no edge in common. Equivalent statement here Main question: ...