Centered colorings in minor-closed graph classes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916695277305856 |
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| author | Hodor, Jędrzej La, Hoang Micek, Piotr Rambaud, Clément |
| author_facet | Hodor, Jędrzej La, Hoang Micek, Piotr Rambaud, Clément |
| contents | A vertex coloring $φ$ of a graph $G$ is $p$-centered if for every connected subgraph $H$ of $G$, either $φ$ uses more than $p$ colors on $H$, or there is a color that appears exactly once on $H$. We prove that for every fixed positive integer $t$, every $K_t$-minor-free graph admits a $p$-centered coloring using $\mathcal{O}(p^{t-1})$ colors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Centered colorings in minor-closed graph classes Hodor, Jędrzej La, Hoang Micek, Piotr Rambaud, Clément Combinatorics Discrete Mathematics A vertex coloring $φ$ of a graph $G$ is $p$-centered if for every connected subgraph $H$ of $G$, either $φ$ uses more than $p$ colors on $H$, or there is a color that appears exactly once on $H$. We prove that for every fixed positive integer $t$, every $K_t$-minor-free graph admits a $p$-centered coloring using $\mathcal{O}(p^{t-1})$ colors. |
| title | Centered colorings in minor-closed graph classes |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2411.02122 |