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 -tidy graphs and -graphs, for every fixed . These classes include cographs, -sparse and -lite graphs. All these coloring problems are known to be NP-hard for general graphs. These algorithms are fixed parameter tractable on the parameter , which is the minimum such that is a -graph. We also prove that every connected -graph with at least vertices is 2-clique-colorable and that every acyclic coloring of a cograph is also nonrepetitive.
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}
}