Introduction to algorithms
Some results on the achromatic number
Journal of Graph Theory
The achromatic number of bounded degree trees
Discrete Mathematics
Approximation algorithms for the achromatic number
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Extremal Graph Theory
On approximating the achromatic number
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Efficient approximation algorithms for the achromatic number
Theoretical Computer Science - Approximation and online algorithms
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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.