Abstract
The achromatic number problem is as follows: given a graph G = (V,E), find the greatest number of colors in a coloring of the vertices of G such that adjacent vertices get distinct colors and for every pair of colors some vertex of the first color and some vertex of the second color are adjacent. This problem is NP-complete even for trees.We present improved polynomial time approximation algorithms for the problem on graphs with large girth and for trees, and linear time approximation algorithms for trees with bounded maximum degree.We also improve the lower bound of Farber et al. for the achromatic number of trees with maximum degree bounded by three.
The author is supported by Deutsche Forschungsgemeinschaft (DFG) as a member of the Graduiertenkolleg Informatik, Universität des Saarlandes, Saarbrücken.
Partially supported by Komitet Badań Naukowych, grant 8 T11C 032 15.
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© 1999 Springer-Verlag Berlin Heidelberg
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Krysta, P., Loryś, K. (1999). Efficient Approximation Algorithms for the Achromatic Number. In: Nešetřil, J. (eds) Algorithms - ESA’ 99. ESA 1999. Lecture Notes in Computer Science, vol 1643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48481-7_35
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DOI: https://doi.org/10.1007/3-540-48481-7_35
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