On the Minimum Sum Coloring of P 4-Sparse Graphs

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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...

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Detalles Bibliográficos
Autores principales: Bonomo, F., Valencia-Pabon, M.
Formato: INPR
Lenguaje:English
Materias:
Graph coloring
Minimum sum coloring
P 4-sparse graphs
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09110119_v_n_p1_Bonomo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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. © 2012 Springer Japan.

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