A Note on Perfect Matchings in Uniform Hypergraphs

We determine the exact minimum -degree threshold for perfect matchings in k-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than 1 2 n k− . This extends our previous results that determine the minimum -degree thresholds for perfect matchings in k-uniform hypergraphs for all ≥ k/2 and provides two new (exact) thresholds: (k, ) = (5, 2) and (7, 3).

• Type: Journal
• Year: 2016
• Where: COMBINATORICS
• Authors: Andrew Treglown, Yi Zhao
• Keywords: COMBINATORICS 2016