Polynomial-Time Perfect Matchings in Dense Hypergraphs

被引：0
|
作者：
Keevash, Peter [1 ]
Knox, Fiachra [1 ]
Mycroft, Richard [2 ]
机构：
[1] Queen Mary Univ London, Sch Math Sci, London E1 4NS, England
[2] Univ Birmingham, Sch Math, Birmingham B31 4AF, W Midlands, England
来源：
STOC'13: PROCEEDINGS OF THE 2013 ACM SYMPOSIUM ON THEORY OF COMPUTING | 2013年
基金：
欧洲研究理事会; 英国工程与自然科学研究理事会;
关键词：
Perfect Matchings; Lattices; UNIFORM HYPERGRAPHS;
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let H be a k-graph on n vertices, with minimum codegree at least n/k + cn for some fixed c > 0. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in H or a certificate that none exists. This essentially solves a problem of Karpinski, Rucinski and Szymanska, who previously showed that this problem is NP-hard for a minimum codegree of n/k - cn. Our algorithm relies on a theoretical result of independent interest, in which we characterise any such hypergraph with no perfect matching using a family of lattice-based constructions.
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页码：311 / 320
页数：10
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