Towards a hypergraph version of the Pósa-Seymour conjecture

0573794 - ÚI 2024 US eng V - Research Report
Pavez-Signé, M. - Sanhueza-Matamala, Nicolás - Stein, M.
Towards a hypergraph version of the Pósa-Seymour conjecture.
Cornell University: Cornell University, 2023. 29 s. arXiv.org e-Print archive, arXiv:2110.09373.
R&D Projects: GA ČR(CZ) GA19-08740S
Institutional support: RVO:67985807
https://arxiv.org/abs/2110.09373

We prove that for fixed r≥k≥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 Pósa-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.
Permanent Link: https://hdl.handle.net/11104/0344149