Positive Codegree Thresholds for Perfect Matchings in Hypergraphs

Abstract. We give, for each [Formula: see text], the precise best possible minimum positive codegree condition for a perfect matching in a large [Formula: see text]-uniform hypergraph [Formula: see text] on [Formula: see text] vertices. Specifically, we show that if [Formula: see text] is sufficiently large and divisible by [Formula: see text] and [Formula: see text] has minimum positive codegree [Formula: see text] and no isolated vertices, then [Formula: see text] contains a perfect matching. For [Formula: see text], this was previously established by Halfpap and Magnan [ Positive Co-Degree Thresholds for Spanning Structures, 2024], who also gave bounds for [Formula: see text] which were tight up to an additive constant.