Coloring of the dth power of the face-centered cubic grid

使用 $O(p)$ 种颜色对网格进行 $p$-中心着色

A $p$-centered coloring for the grid using $O(p)$ colors

本文针对平面网格图，提出了一种使用 $O(p)$ 种颜色进行 $p$-中心着色的显式构造方法。

minor-封闭图类中的中心着色

Centered colorings in minor-closed graph classes

针对minor-封闭图类中的中心着色问题，证明了对固定正整数t，所有不含K_t-子式的图可通过p-中心着色使用O(p^{t-1})种颜色，为该类图的着色提供了复杂度结果。

以中心色染和弱色数在小图闭合图类中的研究

Centered colorings and weak coloring numbers in minor-closed graph classes

本文研究了在排除特定小图的图类中，q-中心色数和q阶弱色数的上界，证明了在O(q)因子内可确定，并在排除平面图时达到常数因子。结果改进了K_t-无小图图的q-中心色数界。

Polynomial bounds for centered colorings on proper minor-closed graph classes

For $p\in \mathbb{N}$, a coloring $λ$ of the vertices of a graph $G$ is {\em{$p$-centered}} if for every connected subgraph~$H$ of $G$, either $H$ receives more than $p$ colors under $λ$ or there is a color that appears exactly once in $H$. In this paper, we prove that every $K_t$-minor-free graph admits a $p$-centered coloring with $\mathcal{O}(p^{g(t)})$ colors for some function $g$. In the special case that the graph is embeddable in a fixed surface $Σ$ we show that it admits a $p$-centered coloring with $\mathcal{O}(p^{19})$ colors, with the degree of the polynomial independent of the genu…

$p$-中心染色的两个下界

Two lower bounds for $p$-centered colorings

本文针对$p$-中心染色问题，构造了浅次图平均度多项式有界的单调图类，证明其所需颜色数超多项式于$p$；并证明最大度$\Delta$的图存在下界$\Omega(\Delta^{2-1/p} p \ln^{-1/p}\Delta)$，匹配已知上界至对数因子。