Matchings in 3-uniform hypergraphs

Details Matchings in 3-uniform hypergraphs Matchings in 3-uniform hypergraphs

2010-09-07

arxiv.org/abs/1009.1298v1

Mathematics

Combinatorics

17 pages, 1 figure

Scientific paper

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 \binom{n-1}{2}-\binom{2n/3}{2}, 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\le n/3 if its minimum vertex degree is greater than \binom{n-1}{2}-\binom{n-d}{2}, which is also best possible.

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