Exact Minimum $d$-Degree Thresholds for Hypergraph Perfect Matchings

Abstract

For fixed integers $k\ge 3$ and $1\le d\le k-1$ and sufficiently large $n\in k\mathbb{N}$, we establish the sharp minimum $d$-degree thresholds that forces perfect matching in every $n$-vertex $k$-uniform hypergraphs. This was conjectued by Treglown and Zhao, and the $d=1$ case was conjectued by Kühn, Osthus and Treglown.

11 pages. Comments welcome