PreprintarXiv licencearXiv
A Chvátal-type codegree condition for Hamiltonian cycles in k-uniform hypergraphs
Abstract
We prove an asymptotic Chvátal-type codegree criterion for tight Hamiltonian cycles in k-uniform hypergraphs for every fixed k≥3. The criterion allows small degrees to be compensated by large degrees in the link graphs of (k−2)-tuples. It strengthens the asymptotic Dirac-type theorem by Rödl, Ruciński and Szemerédi and implies a Pósa-type criterion conjectured by Schülke.
Related
- A Fan-Type Theorem for Hamiltonian Berge Cycles in 3-Uniform Hypergraphs
- A Chvátal--Erdős type condition for supereulerian digraphs with α2=4
- A near-linear Chvátal--Erdős condition for Hamilton cycles in digraphs
- Phase transition of random non-uniform hypergraphs
- Irregular Triads in 3-Uniform Hypergraphs
BibTeX
@misc{zhang2026chvátaltype,
title = {{A Chvátal-type codegree condition for Hamiltonian cycles in $k$-uniform hypergraphs}},
author = {Lu-Ming Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08613},
eprint = {2609.08613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08613},
}
RIS
TY - UNPB
TI - A Chvátal-type codegree condition for Hamiltonian cycles in k-uniform hypergraphs
AU - Lu-Ming Zhang
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08613
UR - https://arxiv.org/abs/2609.08613
AB - We prove an asymptotic Chvátal-type codegree criterion for tight Hamiltonian cycles in k-uniform hypergraphs for every fixed k≥3. The criterion allows small degrees to be compensated by large degrees in the link graphs of (k−2)-tuples. It strengthens the asymptotic Dirac-type theorem by Rödl, Ruciński and Szemerédi and implies a Pósa-type criterion conjectured by Schülke.
ER -