Matchings in hypergraphs of large minimum degree

It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for hypergraphs. We also prove several related results which guarantee the existence of almost perfect matchings in r-uniform hypergraphs of large minimum degree. Our bounds on the minimum degree are essentially best possible.

• Type: Journal
• Year: 2006
• Where: JGT
• Authors: Daniela Kühn, Deryk Osthus
• Keywords: Bipartite Graph, JGT 2006, Minimum Degree, Perfect Matchings