On Hamiltonian cycles in hypergraphs with dense link graphs

Abstract

We show that every $k$-uniform hypergraph on $n$ vertices whose minimum $(k-2)$-degree is at least $(5/9+o(1))n^2/2$ contains a Hamiltonian cycle. A construction due to Han and Zhao shows that this minimum degree condition is optimal. The same result was proved independently by Lang and Sahueza-Matamala.Comment: Dedicated to Endre Szemer\'edi on the occasion of his 80th birthda