A GENERALIZATION OF HALL’S THEOREM FOR k-UNIFORM k-PARTITE HYPERGRAPHS

In this paper we prove a generalized version of hall’s theorem in graphs, for hypergraphs. more precisely, let h be a k-uniform k-partite hypergraph with some ordering on parts as v1, v2, . . . , vk such that the subhypergraph generated on ∪^k−1 i=1 vi has a unique perfect matching. in this case, we give a necessary and sufficient condition for having a matching of size t = |v1| in h. some relevant results and counterexamples are given as well.