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Perfect Matchings in Random r-regular, s-uniform Hypergraphs

Published online by Cambridge University Press:  12 September 2008

Colin Cooper ,
Alan Frieze ,
Michael Molloy  and
Bruce Reed
Colin Cooper
Affiliation:
School of Mathematical Sciences, University of North London, London, UK
Alan Frieze
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Michael Molloy
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Bruce Reed
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
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Abstract

We show that r-regular, s-uniform hypergraphs contain a perfect matching with high probability (whp), provided The Proof is based on the application of a technique of Robinson and Wormald [7, 8]. The space of hypergraphs is partitioned into subsets according to the number of small cycles in the hypergraph. The difference in the expected number of perfect matchings between these subsets explains most of the variance of the number of perfect matchings in the space of hypergraphs, and is sufficient to prove existence (whp), using the Chebychev Inequality.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 1 , March 1996 , pp. 1 - 14
Copyright
Copyright © Cambridge University Press 1996

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