Loose Hamiltonicity
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915664066772992 |
|---|---|
| author | Lang, Richard Sanhueza-Matamala, Nicolás |
| author_facet | Lang, Richard Sanhueza-Matamala, Nicolás |
| contents | We study the appearance of Hamilton $\ell$-cycles in dense $k$-uniform hypergraphs when $\ell \leq k-2$ and $k-\ell$ does not divide $k$. Our main result reduces this problem to the robust existence of a connected $\ell$-cycle tiling in host graph families that are approximately closed under subsampling. As an application, we determine the minimum $d$-degree threshold for $d=k-2$ and all $1 \leq \ell \leq k-2$ when $k - \ell$ does not divide $k$. We also reduce the case $\ell < d$ entirely to the corresponding (non-connected) $\ell$-cycle tiling problem. In addition, our outcomes lead to counting and random robust versions of these results. The proofs are based on the recently introduced method of blow-up covers and thus avoid the use of the Regularity Lemma and the Absorption Method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loose Hamiltonicity Lang, Richard Sanhueza-Matamala, Nicolás Combinatorics 05C35, 05C45, 05C65, 05C70 We study the appearance of Hamilton $\ell$-cycles in dense $k$-uniform hypergraphs when $\ell \leq k-2$ and $k-\ell$ does not divide $k$. Our main result reduces this problem to the robust existence of a connected $\ell$-cycle tiling in host graph families that are approximately closed under subsampling. As an application, we determine the minimum $d$-degree threshold for $d=k-2$ and all $1 \leq \ell \leq k-2$ when $k - \ell$ does not divide $k$. We also reduce the case $\ell < d$ entirely to the corresponding (non-connected) $\ell$-cycle tiling problem. In addition, our outcomes lead to counting and random robust versions of these results. The proofs are based on the recently introduced method of blow-up covers and thus avoid the use of the Regularity Lemma and the Absorption Method. |
| title | Loose Hamiltonicity |
| topic | Combinatorics 05C35, 05C45, 05C65, 05C70 |
| url | https://arxiv.org/abs/2512.08837 |