• Corpus ID: 239016066

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

@inproceedings{PavezSigne2021TowardsAH,
  title={Towards a hypergraph version of the P\'osa-Seymour conjecture},
  author={Mat'ias Pavez-Sign'e and Nicol{\'a}s Sanhueza-Matamala and Maya Jakobine Stein},
  year={2021}
}
We prove that for fixed r > k > 2, every k-uniform hypergraph on n vertices having minimum codegree at least (1 − ( ( r−1 k−1 ) + ( 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… 

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