Co-degree threshold for rainbow perfect matchings in uniform hypergraphs

Abstract

Let $k$ and $n$ be two integers, with $k\ge 3$, $n\equiv 0(\mathrm{mod}k)$, and $n$ sufficiently large. We determine the $(k-1)$-degree threshold for the existence of a rainbow perfect matchings in $n$-vertex $k$-uniform hypergraph. This implies the result of Rödl, Ruciński, and Szemerédi on the $(k-1)$-degree threshold for the existence of perfect matchings in $n$-vertex $k$-uniform hypergraphs. In our proof, we identify the extremal configurations of closeness, and consider whether or not the hypergraph is close to the extremal configuration. In addition, we also develop a novel absorbing device and generalize the absorbing lemma of Rödl, Ruciński, and Szemerédi.

References in corpus (2)

• Global hypercontractivity and its applications
• Rainbow perfect matchings for 4-uniform hypergraphs