A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs

Natalie Behague; Felix Christian Clemen; Joseph Hyde; Natasha Morrison

A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs

Combinatorics 2026-07-31 v1

Authors: Natalie Behague , Felix Christian Clemen , Joseph Hyde , Natasha Morrison

Abstract

We determine the asymptotically best possible minimum vertex degree condition forcing a two-coloured $3$ -graph to contain a colour-biased tight Hamilton cycle. This confirms a conjecture of H\`an, Lang, Marciano, Pavez-Sign\'e, Sanhueza-Matamala, Treglown and Z\'arate-Guer\'en.

Cite

@article{arxiv.2607.29628,
  title  = {A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs},
  author = {Natalie Behague and Felix Christian Clemen and Joseph Hyde and Natasha Morrison},
  journal= {arXiv preprint arXiv:2607.29628},
  year   = {2026}
}