Minimum degree thresholds for Hamilton (k/2)-cycles in k-uniform hypergraphs

Abstract

For any even integer k≥6, integer d such that k/2≤d≤k−1, and sufficiently large n∈(k/2)N, we find a tight minimum d-degree condition that guarantees the existence of a Hamilton (k/2)-cycle in every k-uniform hypergraph on n vertices. When n∈kN, the degree condition coincides with the one for the existence of perfect matchings provided by Rödl, Ruciński and Szemerédi (for d=k−1) and Treglown and Zhao (for d≥k/2), and thus our result strengthens theirs in this case.