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arXiv · 2603.28202

Towards Pósa's Conjecture for $3$-graphs

Debmalya Bandyopadhyay·Allan Lo·Richard Mycroft
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Abstract

We prove that every $3$-graph $H$ on $n$ vertices with minimum codegree $δ_2(H) \geq 7n/9 + o(n)$ contains the square of a tight Hamilton cycle. This strengthens a theorem of Bedenknecht and Reiher that $δ_2(H) \geq 4n/5 + o(n)$ is sufficient. The central novelty of our arguments is an improved understanding of the connectivity structure of $3$-graphs with large minimum codegree.

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Debmalya Bandyopadhyay, Allan Lo, Richard Mycroft. 2026-03-30. Towards Pósa's Conjecture for $3$-graphs. https://arxiv.org/abs/2603.28202

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