Counting tight Hamilton cycles in Dirac hypergraphs
Combinatorics
2026-04-17 v1
Abstract
Suppose is a -uniform hypergraph on vertices such that every -subset of belongs to at least edges, where . Let denote the number of tight Hamilton cycles in , that is, cyclic orderings of in which every consecutive vertices form an edge. We prove that , where is the hypergraph entropy of , defined via perfect fractional matchings. This bound is tight, for example, for all (nearly) regular hypergraphs, in particular for the binomial random hypergraph. It also implies a conjecture by Ferber, Hardiman and Mond, stating that .
Keywords
Cite
@article{arxiv.2604.14978,
title = {Counting tight Hamilton cycles in Dirac hypergraphs},
author = {Felix Joos and Xinyue Xie},
journal= {arXiv preprint arXiv:2604.14978},
year = {2026}
}
Comments
23 pages + 9 pages appendix for general l-cycles