Exact minimum degree thresholds for perfect matchings in uniform hypergraphs II

Abstract

Given positive integers k⩾3 and ℓ where k/2⩽ℓ⩽k−1, we give a minimum ℓ-degree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result, and extends work of Rödl, Ruciński and Szemerédi who determined the threshold for ℓ=k−1. Our approach makes use of the absorbing method, and builds on earlier work, where we proved the result for k divisible by 4.