Minimum sum set coloring of trees and line graphs of trees

In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph i...

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Detalles Bibliográficos
Autores: Bonomo, Flavia, Duran, Guillermo Alfredo, Marenco, Javier, Valencia Pabon, Mario
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2011
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/15019
Acceso en línea:http://hdl.handle.net/11336/15019
Access Level:acceso abierto
Palabra clave:Graph Coloring
Minimum Sum Coloring
Set-Coloring
Trees
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.