Minimum sum set coloring of trees and line graphs of trees

• Autores: Bonomo, F.; Durn, G.; Marenco, J.; Valencia-Pabon, M.
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Discrete Appl Math 2011;159(5):288-294
• Materia: Graph coloring; Line graphs of trees; Minimum sum coloring; Set-coloring; Trees; Graph colorings; Line graph; Minimum sum coloring; Set-coloring; Trees; Coloring; Graph theory; Graphic methods; Trees (mathematics)
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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. © 2010 Elsevier B.V. All rights reserved.
Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil:Marenco, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.