On the Minimum Sum Coloring of P_4-sparse graphs

BONOMO, FLAVIA; VALENCIA-PABON, MARIO

GRAPHS AND COMBINATORICS

SPRINGER TOKYO

Lugar: Tokyo; Año: 2014 vol. 30 p. 303 - 314

0911-0119

In this paper, we study the Minimum Sum Coloring (MSC) problem on $P_4$-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 $P_4$-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 $P_4$-sparse graphs.