Geodesic
Towards a hypergraph version of the Pósa-Seymour conjecture
Advances in Combinatronics (2023)

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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.
Publié le : 
@article{ADVC_2023_a4,
     author = {Mat{\'\i}as Pavez-Sign\'e and Nicol\'as Sanhueza-Matamala and Maya Stein},
     title = {Towards a hypergraph version of the {P\'osa-Seymour} conjecture},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2023_a4/}
}
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%A Maya Stein
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Matías Pavez-Signé; Nicolás Sanhueza-Matamala; Maya Stein. Towards a hypergraph version of the Pósa-Seymour conjecture. Advances in Combinatronics (2023). http://geodesic.mathdoc.fr/item/ADVC_2023_a4/