Hall's Theorem(graph theory form) A bipartite graph G(U,V,E)has a matching of U → IN(S)l≥ISI for all SCU matching:edge independent set MCE with no e1,e2EM share a vertex N(S)={v|]u∈S,uw∈E} Hall’s Theorem (graph theory form) A bipartite graph G(U,V,E) has a matching of U |N(S)| ≥ |S| for all S⊆U U V matching: edge independent set M⊆E with no e1,e2∈M share a vertex N(S) = {v | ∃u∈S, uv∈E}