Perfect Matchings in 4-uniform hypergraphs

Abstract

A perfect matching in a 4-uniform hypergraph is a subset of $\lfloor \frac{n}{4}\rfloor$ disjoint edges. We prove that if $H$ is a sufficiently large 4-uniform hypergraph on $n=4k$ vertices such that every vertex belongs to more than $\left(\genfrac{}{}{0ex}{}{n-1}{3}\right)-\left(\genfrac{}{}{0ex}{}{3n/4}{3}\right)$ edges then $H$ contains a perfect matching. This bound is tight and settles a conjecture of H{á}n, Person and Schacht.

References in corpus (1)

• Perfect matching in 3-uniform hypergraphs with large vertex degree

Cited by in corpus (10)

• Fractional and integer matchings in uniform hypergraphs
• Polynomial-time perfect matchings in dense hypergraphs
• Near Perfect Matchings in $k$-uniform Hypergraphs
• Perfect matching in 3-uniform hypergraphs with large vertex degree
• Perfect Packings in Quasirandom Hypergraphs II
• Matchings in 3-uniform hypergraphs
• Large matchings in uniform hypergraphs and the conjectures of Erdos and Samuels
• Minimum codegree threshold for $C_6^3$-factors in $3$-uniform Hypergraphs
• Minimum vertex degree threshold for $C_4^3$-tiling
• Packing k-partite k-uniform hypergraphs