Abstract
In this paper, we study the optimum cost chromatic partition (OCCP) problem for several graph classes. The OCCP problem is the problem of coloring the vertices of a graph such that adjacent vertices get different colors and that the total coloring costs are minimum.
First, we prove that the OCCP problem graphs with constant treewidth k can be solved in O(¦V¦·(log ¦V¦)k+1) time, respectively. Next, we study an ILP formulation of the OCCP problem given by Sen et al. [9]. We show that the corresponding polyhedron contains only integral 0/1 extrema if and only if the graph G is a diamond — free chordal graph. Furthermore, we prove that the OCCP problem is NP-complete for bipartite graphs. Finally, we show that the precoloring extension and the OCCP problem are NP-complete for permutation graphs.
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© 1997 Springer-Verlag Berlin Heidelberg
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Jansen, K. (1997). The optimum cost chromatic partition problem. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_58
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DOI: https://doi.org/10.1007/3-540-62592-5_58
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