Bounds and Fixed-Parameter Algorithms for Weighted Improper Coloring (Extended Version)
Abstract
We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by pathwidth. We generalize bounds for defective coloring to weighted improper coloring and give a bound for weighted improper coloring in terms of the sum of edge weights. Finally we give fixed-parameter algorithms for weighted improper coloring both when parameterized by treewidth and maximum degree and when parameterized by treewidth and precision of edge weights. In particular, we obtain a linear-time algorithm for weighted improper coloring of interval graphs of bounded degree.
Cite
@article{arxiv.1509.00099,
title = {Bounds and Fixed-Parameter Algorithms for Weighted Improper Coloring (Extended Version)},
author = {Bjarki Ágúst Guðmundsson and Tómas Ken Magnússon and Björn Orri Sæmundsson},
journal= {arXiv preprint arXiv:1509.00099},
year = {2015}
}
Comments
18 pages, 5 figures, extended version for additional proofs in appendix for 16th Italian Conference on Theoretical Computer Science 2015