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Matchings in hypergraphs of large minimum degree

By Daniela Kühn and Deryk Osthus


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.

Year: 2013
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