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arXiv · 2411.02122

Centered colorings in minor-closed graph classes

Jędrzej Hodor·Hoang La·Piotr Micek·Clément Rambaud
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Abstract

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.

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Jędrzej Hodor, Hoang La, Piotr Micek, Clément Rambaud. 2025-04-18. Centered colorings in minor-closed graph classes. https://arxiv.org/abs/2411.02122

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