An upper bound for the equitable chromatic number of complete n-partite graphs

A proper vertex coloring of a graph $G$ is equitable if the size of color classes differ by at most one. The equitable chromatic number of $G$ is the smallest integer $m$ such that $G$ is equitable m-colorable. In this paper, we derive an upper bound for the equitable chromatic number of complete n-partite graph $K_{p_{1},p_{2}, ... ,p_{n}}$

Obituary - Richard Kenneth Guy, 1916-2020

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Equitable and proportional coloring of trees

We show that almost all trees can be equitably 3-colored, that is, with three color classes of cardinalities differing by at most one. Also, except in some extreme cases, they can be 3-colored with color classes of sizes in given proportions. © 1983