Perfect matchings in 3-partite 3-uniform hypergraphs

TL;DR

This paper establishes a precise degree threshold condition for the existence of perfect matchings in 3-partite 3-uniform hypergraphs, advancing understanding of combinatorial structures in hypergraph theory.

Contribution

It provides the first exact Dirac-type vertex degree threshold for perfect matchings in 3-partite 3-uniform hypergraphs.

Findings

Determines the exact degree threshold for perfect matchings.

Extends Dirac-type theorems to hypergraph settings.

Offers new insights into hypergraph matching conditions.

Abstract

Let $H$ be a $3$-partite $3$-uniform hypergraph, i.e. a $3$-uniform hypergraph such that every edge intersects every partition class in exactly one vertex, with each partition class of size $n$. We determine a Dirac-type vertex degree threshold for perfect matchings in $3$-partite $3$-uniform hypergraphs.