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

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