An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs. Recall that the latter are graphs in which each 2-connected component is a complete graph. The problem remains hard in the class of block graphs. In this paper, we present some graph theoretic results relating various parameters. Then we use them in order to trace some algorithmic implications, mainly dealing with the fixed-parameter tractability of the problem.

翻译：图形 $G= (V, E) 的公平彩色是( proper) 顶端彩色 $G $( proper) 的 顶端彩色 $G $( g$), 这样任何两个彩色等级的大小都会因最多一个颜色而不同 。 在本文中, 我们考虑区块图中的公平彩色问题 。 回顾后者是图表, 每个与2 连接的组件都是完整的图形 。 在块图的类别中, 问题仍然很棘手 。 在本文中, 我们提出一些图表与各种参数相关的理论结果 。 然后我们用它们来追踪某些算法影响, 主要是处理问题的固定参数可移动性 。