A $p$-centered coloring of a graph $G$, where $p$ is a positive integer, is a coloring of the vertices of $G$ in such a way that every connected subgraph of $G$ either contains a vertex with a unique color or contains more than $p$ different colors. We give an explicit construction of a $p$-centered coloring using $O(p)$ colors for the planar grid.

翻译：$p$-中心染色是图$G$的一种顶点染色方案，其中$p$为正整数，要求图$G$的每个连通子图要么包含一个具有唯一颜色的顶点，要么包含超过$p$种不同颜色。本文针对平面网格给出了一个使用$O(p)$种颜色的$p$-中心染色的显式构造。