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Tree-coloring problems of bounded treewidth graphs

Author

Listed:
  • Bi Li

    (Xidian University)

  • Xin Zhang

    (Xidian University)

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.

Suggested Citation

  • Bi Li & Xin Zhang, 2020. "Tree-coloring problems of bounded treewidth graphs," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 156-169, January.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:1:d:10.1007_s10878-019-00461-7
    DOI: 10.1007/s10878-019-00461-7
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    References listed on IDEAS

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    1. Guantao Chen & Yuping Gao & Songling Shan & Guanghui Wang & Jianliang Wu, 2017. "Equitable vertex arboricity of 5-degenerate graphs," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 426-432, August.
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