Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II

A. Treglown, Y. Zhao

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

Given positive integers k ≥ 3 and ℓ where 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, and extends work of Rödl, Ruciński and Szemerédi who determined the threshold for ℓ = k - 1. Our approach makes use of the absorbing method, and builds on earlier work, where we proved the result for k divisible by 4.
Original languageEnglish
Pages (from-to)1463-1482
Number of pages20
JournalJournal of Combinatorial Theory, Series A
Volume120
Issue number7
DOIs
Publication statusPublished - 1 Sept 2013

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