Tree-coloring problems of bounded treewidth graphs

Abstract

This paper studies the parameterized complexity of the tree-coloring problem and equitable tree-coloring problem. Given a graph $$G=(V,E)$$ and an integer $$r \ge 1$$, we give an FPT algorithm to decide whether there is a tree-r-coloring of graph G when parameterized by treewidth. Moreover, we prove that to decide the existence of an equitable tree-r-coloring of graph G is W[1]-hard when parameterized by treewidth; and that it is polynomial solvable in the class of graphs with bounded treewidth.