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arXiv · 2110.09373

Towards a hypergraph version of the P\'osa-Seymour conjecture

Matías Pavez-Signé·Nicolás Sanhueza-Matamala·Maya Stein
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Abstract

We prove that for fixed $r\ge k\ge 2$, every $k$-uniform hypergraph on $n$ vertices having minimum codegree at least $(1-(\binom{r-1}{k-1}+\binom{r-2}{k-2})^{-1})n+o(n)$ contains the $(r-k+1)$th power of a tight Hamilton cycle. This result may be seen as a step towards a hypergraph version of the P\'osa-Seymour conjecture. Moreover, we prove that the same bound on the codegree suffices for finding a copy of every spanning hypergraph of tree-width less than $r$ which admits a tree decomposition where every vertex is in a bounded number of bags.

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Matías Pavez-Signé, Nicolás Sanhueza-Matamala, Maya Stein. 2021-10-18. Towards a hypergraph version of the P\'osa-Seymour conjecture. https://doi.org/10.19086/aic.2023.3

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