Minimum sum set coloring of trees and line graphs of trees |
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| Authors: | Flavia Bonomo,Guillermo Durá n,Javier Marenco,Mario Valencia-Pabon |
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| Affiliation: | a CONICET, Argentinab Departamento de Computación, FCEN, Universidad de Buenos Aires, Argentinac Departamento de Matemática, FCEN, Universidad de Buenos Aires, Argentinad Departamento de Ingeniería Industrial, FCFM, Universidad de Chile, Chilee Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentinaf LIPN, Université Paris-Nord, France |
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| Abstract: | 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. |
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| Keywords: | Graph coloring Minimum sum coloring Set-coloring Trees Line graphs of trees |
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