English

Fixed parameter algorithms for restricted coloring problems

Discrete Mathematics 2011-09-14 v2 Computational Complexity Data Structures and Algorithms

Abstract

In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number, the Thue chromatic number, the harmonious chromatic number and the clique chromatic number of P4P_4-tidy graphs and (q,q4)(q,q-4)-graphs, for every fixed qq. These classes include cographs, P4P_4-sparse and P4P_4-lite graphs. All these coloring problems are known to be NP-hard for general graphs. These algorithms are fixed parameter tractable on the parameter q(G)q(G), which is the minimum qq such that GG is a (q,q4)(q,q-4)-graph. We also prove that every connected (q,q4)(q,q-4)-graph with at least qq vertices is 2-clique-colorable and that every acyclic coloring of a cograph is also nonrepetitive.

Keywords

Cite

@article{arxiv.1107.0056,
  title  = {Fixed parameter algorithms for restricted coloring problems},
  author = {Victor Campos and Cláudia Linhares-Sales and Ana Karolinna Maia and Nicolas Martins and Rudini Menezes Sampaio},
  journal= {arXiv preprint arXiv:1107.0056},
  year   = {2011}
}
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