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 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.
KeywordsGraph coloring Minimum sum coloring P4-sparse graphs
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- 3.Bonomo, F., Valencia-Pabon, M.: Minimum sum coloring of P 4-sparse graphs. In: Proceedings pf V Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS), Electronic Notes in Discrete Mathematics, vol. 35, pp. 293–298. Elsevier, Amsterdam (2009)Google Scholar
- 5.Giaro, K., Janczewski, R., Kubale, M., Malafiejski, M: A 27/26-approximation algorithm for the chromatic sum coloring of bipartite graphs. In: Proceedings of 5th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX), Lecture Notes in Computer Science, vol. 2462, pp. 135–145. Springer, Berlin (2002)Google Scholar
- 7.Hoà àng, C.T.: Perfect graphs. Thesis, School of Computer Science, McGill University (1985)Google Scholar
- 11.Jansen, K.: Complexity results for the optimum cost chromatic partition problem.In: Proceedings of 24th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science, vol. 1256, pp. 727–737. Springer, Berlin (1997)Google Scholar
- 12.Kubick, E.: The chromatic sum of a graph. Thesis, Western Michigan University (1989)Google Scholar
- 13.Kubicka, E., Schwenk, A.J. An introduction to chromatic sums. In: Proceedings of 17th ACM Annual Computer Science Conference, pp. 39–45 (1989)Google Scholar
- 15.Salavatipour, M.: On sum coloring of graphs. Master’s thesis, Department of Computer Science, University of Toronto (2000)Google Scholar