Gy{\'a}rf{\'a}s et al. and Zaker have proven that the Grundy number of a graph $G$ satisfies $\Gamma(G)\ge t$ if and only if $G$ contains an induced subgraph called a $t$-atom.The family of $t$-atoms has bounded order and contains a finite number of graphs.In this article, we introduce equivalents of $t$-atoms for b-coloring and partial Grundy coloring.This concept is used to prove that determining if $\varphi(G)\ge t$ and $\partial\Gamma(G)\ge t$ (under conditions for the b-coloring), for a graph $G$, is in XP with parameter $t$.We illustrate the utility of the concept of $t$-atoms by giving results on b-critical vertices and edges, on b-perfect graphs and on graphs of girth at least $7$.
翻译：Gy\'a}rf\'a}以及他人和Zaker已经证明,如果而且只有$G$包含一个称为$t$的诱导子图,G$的格伦迪数字才能满足$Gmma(G)\ge t$。$t$的组别已经绑定了顺序并包含一定数量的图表。在本篇文章中,我们为b色和部分粗度颜色引入等值$t$-atom。这个概念用来证明确定$\varphi(G)\ge t$和$\part\G)\gma(G)\ge$t$(在b-颜色条件下)是否是美元和$B-colorning(G)\ge$ t$(G)\ge$)。我们通过在b-临界脊椎和边缘、b-perfect 图形和 girth 图表上至少7美元的结果来说明$tams概念的效用。
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