Tree-coloring problems of bounded treewidth graphs

Bi Li () and Xin Zhang ()
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Bi Li: Xidian University
Xin Zhang: Xidian University

Journal of Combinatorial Optimization, 2020, vol. 39, issue 1, No 11, 156-169

Abstract: Abstract This paper studies the parameterized complexity of the tree-coloring problem and equitable tree-coloring problem. Given a graph $$G=(V,E)$$G=(V,E) and an integer $$r \ge 1$$r≥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.

Keywords: Tree-coloring; Equitable tree-coloring; Nice tree decomposition; Bounded treewidth (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-019-00461-7

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