Perfect matching in 3-uniform hypergraphs with large vertex degree

Abstract

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 $\left(\genfrac{}{}{0ex}{}{n-1}{2}\right)-\left(\genfrac{}{}{0ex}{}{2n/3}{2}\right)+1$ edges then $H$ contains a perfect matching. We give a construction to show that this result is best possible.

arXiv admin note: text overlap with arXiv:1101.5675

References in corpus (2)

• Perfect matchings in r-partite r-graphs
• Perfect Matchings in 4-uniform hypergraphs

Cited by in corpus (6)

• Fractional and integer matchings in uniform hypergraphs
• Polynomial-time perfect matchings in dense hypergraphs
• Perfect Matchings in 4-uniform hypergraphs
• Matchings in 3-uniform hypergraphs
• Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
• Packing k-partite k-uniform hypergraphs