Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:120

Article

Treglown, Andrew¹  Zhao, Yi² 

[1] Univ London, Sch Math Sci, London E1 4NS, England

[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

关键词: Perfect matchings;    Hypergraphs;    Absorbing method;   

DOI  :  10.1016/j.jcta.2013.04.008

来源: Elsevier

【 摘 要 】

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 Rodl, Rucinski and Szemeredi 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free