Matchings in 3-uniform hypergraphs

Authors:
Daniela KüHn;Deryk Osthus;Andrew Treglown
Affiliations:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK;School of Mathematics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK;School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

Citing 8
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Abstract

We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose that H is a sufficiently large 3-uniform hypergraph whose order n is divisible by 3. If the minimum vertex degree of H is greater than (n-12)-(2n/32), then H contains a perfect matching. This bound is tight and answers a question of Han, Person and Schacht. More generally, we show that H contains a matching of size d=