Exact minimum degree thresholds for perfect matchings in uniform hypergraphs

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Abstract

Given positive integers k and where 4 divides k and k/2k1, we give a minimum -degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result. Our approach makes use of the absorbing method, as well as the hypergraph removal lemma and a structural result of Keevash and Sudakov relating to the Turán number of the expanded triangle.

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The second author was supported in part by NSA grant H98230-10-1-0165.