We show that every k-uniform hypergraph on n vertices whose minimum (k−2)-degree is at least (5/9+o(1))n2/2 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.
@article{arxiv.2007.03820,
title = {On Hamiltonian cycles in hypergraphs with dense link graphs},
author = {Joanna Polcyn and Christian Reiher and Vojtěch Rödl and Bjarne Schülke},
journal= {arXiv preprint arXiv:2007.03820},
year = {2022}
}
Comments
Dedicated to Endre Szemer\'edi on the occasion of his 80th birthday