Exact minimum degree thresholds for perfect matchings in uniform hypergraphs

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Abstract

Given positive integers k and ℓ where 4 divides k and k/2 ≤ ℓ ≤ k − 1,
we give a minimum ℓ-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 Tur´an number of the expanded triangle
Original languageEnglish
Pages (from-to)1500-1522
JournalJournal of Combinatorial Theory, Series A
Volume119
Early online date5 May 2012
DOIs
Publication statusPublished - 1 Oct 2012

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