Hall-type theorems for hypergraphs
= Hall-type theorems for hypergraphs
{wiki=Hall-type_theorems_for_hypergraphs}
Hall-type theorems for hypergraphs are generalizations of Hall's Marriage Theorem, which originally deals with bipartite graphs. Hall's theorem states that a perfect matching exists in a bipartite graph if and only if for every subset of vertices in one part, the number of neighbors in the other part is at least as large as the size of the subset.