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.
We prove that there exists no polynomial approximation algorithm with ratio O(|V|0.5−ɛ) for the OCCP problem restricted to bipartite and interval graphs, unless P=NP.
Furthermore, we propose approximation algorithms with ratio O(|V|0.5) for bipartite, interval and unimodular graphs. Finally, we prove that there exists no polynomial approximation algorithm with ratio O(|V|1−ɛ) for the OCCP problem restricted to split, chordal, permutation and comparability graphs, unless P=NP.
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© 1997 Springer-Verlag Berlin Heidelberg
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Jansen, K. (1997). Approximation results for the optimum cost chromatic partition problem. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_226
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DOI: https://doi.org/10.1007/3-540-63165-8_226
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