Graphs and Combinatorics

, Volume 30, Issue 2, pp 303–314 | Cite as

On the Minimum Sum Coloring of P 4-Sparse Graphs

Original Paper


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.


Graph coloring Minimum sum coloring P4-sparse graphs 


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© Springer Japan 2012

Authors and Affiliations

  1. 1.IMAS-CONICET, Departamento de ComputaciónFacultad de Ciencias  Exactas y Naturales, Universidad de Buenos AiresBuenos AiresArgentina
  2. 2.LIPN, Université Paris-NordVilletaneuseFrance

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