Universality for transversal powers of Hamilton cycles
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914105058656256 |
|---|---|
| author | Heath, Emily Hyde, Joseph Morrison, Natasha Ogden, Shannon |
| author_facet | Heath, Emily Hyde, Joseph Morrison, Natasha Ogden, Shannon |
| contents | Let $k \ge 2$ and let $\bf G = \{G_1, \ldots, G_{m}\}$ be a collection of graphs on a common vertex set of cardinality $n$. We show that if each graph in $\bf G$ has minimum degree at least $(1-\frac{1}{2k} + o(1))n$, then for every edge-colouring $χ$ of the $k$th power of a Hamilton cycle $C_n^k$ with $m$ colours, there is a copy of $C_n^k$ in $\bf G$ such that $e \in G_{χ(e)}$ for every edge $e$ in $C_n^k$. This generalises a result of Bowtell, Morris, Pehova, and Staden, who provided asymptotically best possible minimum degree conditions for the Hamilton cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universality for transversal powers of Hamilton cycles Heath, Emily Hyde, Joseph Morrison, Natasha Ogden, Shannon Combinatorics Let $k \ge 2$ and let $\bf G = \{G_1, \ldots, G_{m}\}$ be a collection of graphs on a common vertex set of cardinality $n$. We show that if each graph in $\bf G$ has minimum degree at least $(1-\frac{1}{2k} + o(1))n$, then for every edge-colouring $χ$ of the $k$th power of a Hamilton cycle $C_n^k$ with $m$ colours, there is a copy of $C_n^k$ in $\bf G$ such that $e \in G_{χ(e)}$ for every edge $e$ in $C_n^k$. This generalises a result of Bowtell, Morris, Pehova, and Staden, who provided asymptotically best possible minimum degree conditions for the Hamilton cycle. |
| title | Universality for transversal powers of Hamilton cycles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.18163 |