On Hamiltonian cycles in hypergraphs with dense link graphs

Joanna Polcyn; Christian Reiher; Vojtěch Rödl; Bjarne Schülke

doi:10.1016/j.jctb.2021.04.001

paper

On Hamiltonian cycles in hypergraphs with dense link graphs

arXiv:2007.03820 · doi:10.1016/j.jctb.2021.04.001

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.

Dedicated to Endre Szemerédi on the occasion of his 80th birthday