Towards Pósa's Conjecture for $3$-graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908920685002752 |
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| author | Bandyopadhyay, Debmalya Lo, Allan Mycroft, Richard |
| author_facet | Bandyopadhyay, Debmalya Lo, Allan Mycroft, Richard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Towards Pósa's Conjecture for $3$-graphs Bandyopadhyay, Debmalya Lo, Allan Mycroft, Richard Combinatorics 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. |
| title | Towards Pósa's Conjecture for $3$-graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.28202 |