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.

翻译：我们针对弦图上的最小和着色问题提出了一个$(1.796+\epsilon)$-近似算法，改进了 Gandhi 等人[2005]提出的3.591-近似结果。为此，我们还设计了弦图上最大$k$-可着色子图问题的首个多项式时间近似方案。