Approximate Minimum Sum Colorings and Maximum $k$-Colorable Subgraphs of Chordal Graphs

TL;DR

This paper presents a significant improvement in approximating the minimum sum coloring problem for chordal graphs and introduces the first polynomial-time scheme for maximum k-colorable subgraphs in such graphs.

Contribution

It provides a better approximation ratio for minimum sum coloring and develops the first polynomial-time approximation scheme for maximum k-colorable subgraphs in chordal graphs.

Findings

Achieved a (1.796+ε)-approximation for minimum sum coloring.

Designed the first polynomial-time approximation scheme for maximum k-colorable subgraphs.

Improved previous approximation ratio from 3.591 to 1.796+ε.

Abstract

We give a $(1.796+\epsilon)$-approximation for the minimum sum coloring problem on chordal graphs, improving over the previous 3.591-approximation by Gandhi et al. [2005]. To do so, we also design the first polynomial-time approximation scheme for the maximum $k$-colorable subgraph problem in chordal graphs.