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.
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The first author is supported by the National Natural Science Foundation of China (Nos. 11701440, 11626181), the Natural Science Basic Research Plan in Shaanxi Province of China(No. 2017JQ1031), and the second author is supported by the National Natural Science Foundation of China (No. 11871055)
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Li, B., Zhang, X. Tree-coloring problems of bounded treewidth graphs. J Comb Optim 39, 156–169 (2020). https://doi.org/10.1007/s10878-019-00461-7
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DOI: https://doi.org/10.1007/s10878-019-00461-7