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arXiv · 1509.00099

Bounds and Fixed-Parameter Algorithms for Weighted Improper Coloring (Extended Version)

Bjarki Ágúst Guðmundsson·Tómas Ken Magnússon·Björn Orri Sæmundsson
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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.

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Bjarki Ágúst Guðmundsson, Tómas Ken Magnússon, Björn Orri Sæmundsson. 2015-09-01. Bounds and Fixed-Parameter Algorithms for Weighted Improper Coloring (Extended Version). https://arxiv.org/abs/1509.00099

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