On the Minimum Sum Coloring of P4-sparse graphs

Abstract

In this paper, we study the Minimum Sum Coloring (MSC) problem on P4-sparse graphs. In the MSC problem, we aim to assign natural numbers to vertices of a graph such that adjacent vertices get different numbers, and the sum of the numbers assigned to the vertices is minimum. Based in the concept of maximal sequence associated with an optimal solution of the MSC problem of any graph, we show that there is a large sub-family of P4-sparse graphs for which the MSC problem can be solved in polynomial time. Moreover, we give a parameterized algorithm and a 2-approximation algorithm for the MSC problem on general P4-sparse graphs.