For every k ≥ 3, a large k-uniform hypergraph with minimum positive codegree at least (k−1)/k n − (k−2) and no isolated vertices must contain a perfect matching, and this bound is best possible.
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Positive codegree thresholds for perfect matchings in hypergraphs
For every k ≥ 3, a large k-uniform hypergraph with minimum positive codegree at least (k−1)/k n − (k−2) and no isolated vertices must contain a perfect matching, and this bound is best possible.