Perfect matching in 3 uniform hypergraphs with large vertex degree

Details Perfect matching in 3 uniform hypergraphs with large vertex degree Perfect matching in 3 uniform hypergraphs with large vertex degree

2011-01-30

arxiv.org/abs/1101.5830v2

Computer Science

Discrete Mathematics

Scientific paper

A perfect matching in a 3-uniform hypergraph on $n=3k$ vertices is a subset
of $\frac{n}{3}$ disjoint edges. We prove that if $H$ is a 3-uniform hypergraph
on $n=3k$ vertices such that every vertex belongs to at least ${n-1\choose 2} -
{2n/3\choose 2}+1$ edges then $H$ contains a perfect matching. We give a
construction to show that this result is best possible.

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