A set of edges no two sharing a vertex. König's theorem: in bipartite graphs, max matching = min vertex cover. Hall's marriage theorem: perfect matching iff ∀S ⊆ A, |N(S)| ≥ |S|.
A set of edges no two sharing a vertex. König's theorem: in bipartite graphs, max matching = min vertex cover. Hall's marriage theorem: perfect matching iff ∀S ⊆ A, |N(S)| ≥ |S|.