Equitable Colorings of Bounded Treewidth Graphs

A proper coloring of a graph G is equitable if the sizes of any two color classes differ by at most one. A proper coloring is l-bounded, when each color class has size at most l. We consider the problems to determine for a given graph G (and a given integer l) whether G has an equitable (l-bounded) k-coloring. We prove that both problems can be solved in polynomial time on graphs of bounded treewidth, and show that a precolored version remains NP-complete on trees.

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