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Near Perfect Matchings in k-Uniform Hypergraphs

Published online by Cambridge University Press:  02 October 2014

JIE HAN
JIE HAN*
Affiliation:
Georgia State University, Atlanta, GA 30303, USA (e-mail: jhan22@gsu.edu)
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Abstract

Let H be a k-uniform hypergraph on n vertices where n is a sufficiently large integer not divisible by k. We prove that if the minimum (k − 1)-degree of H is at least ⌊n/k⌋, then H contains a matching with ⌊n/k⌋ edges. This confirms a conjecture of Rödl, Ruciński and Szemerédi [13], who proved that minimum (k − 1)-degree n/k + O(log n) suffices. More generally, we show that H contains a matching of size d if its minimum codegree is d < n/k, which is also best possible.

Keywords

Primary 05C70Secondary 05C50

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 5 , September 2015 , pp. 723 - 732
Copyright
Copyright © Cambridge University Press 2014 

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