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.
Journal of Combinatorial Theory, Series B
Bollobás, B., & Guy, R. (1983). Equitable and proportional coloring of trees. Journal of Combinatorial Theory, Series B, 34 (2), 177-186. https://doi.org/10.1016/0095-8956(83)90017-5