Graph theoretic and algorithmic aspect of the equitable coloring problem in block graphs

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