A vertex coloring $\varphi$ of a graph $G$ is $p$-centered if for every connected subgraph $H$ of $G$, either $\varphi$ 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.

翻译：图$G$的顶点着色$\varphi$称为$p$-中心的，若对$G$的每个连通子图$H$，要么$\varphi$在$H$上使用了超过$p$种颜色，要么存在一种颜色在$H$上恰好出现一次。我们证明：对任意固定的正整数$t$，每个不含$K_t$子式的图都允许使用$\mathcal{O}(p^{t-1})$种颜色的$p$-中心着色。