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...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Recursos: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | inglés |
| OAI Identifier: | paperaa:paper_0166218X_v159_n5_p288_Bonomo |
| Acesso em linha: | http://hdl.handle.net/20.500.12110/paper_0166218X_v159_n5_p288_Bonomo |
| Access Level: | acceso abierto |
| Palavra-chave: | Graph coloring Line graphs of trees Minimum sum coloring Set-coloring Trees Graph colorings Line graph Coloring Graph theory Graphic methods Trees (mathematics) |
| Resumo: | 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. |
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