Concerning the achromatic number of graphs
Journal of Combinatorial Theory Series B
Achromatic number is NP-complete for cographs and interval graphs
Information Processing Letters
Approximating the minimum maximal independence number
Information Processing Letters
A still better performance guarantee for approximate graph coloring
Information Processing Letters
Some results on the achromatic number
Journal of Graph Theory
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Approximation algorithms for the achromatic number
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Efficient Approximation Algorithms for the Achromatic Number
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Extremal Graph Theory
Efficient approximation algorithms for the achromatic number
Theoretical Computer Science - Approximation and online algorithms
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The achromatic number problem is to legally color the vertices of an input graph with the maximum number of colors, denoted &psgr;*, so that every two color classes share at least one edge. This problem is known to be NP-hard.For general graphs we give an algorithm that approximates the achromatic number within ratio of &Ogr;(n ·log log n/ log n). This improves over the previously known approximation ratio of &Ogr;(n/√log n), due to Chaudhary and Vishwanathan [4].For graphs of girth at least 5 we give an algorithm with approximation ratio &Ogr;(min{n1/3, √&psgr;*}). This improves over an approximation ratio &Ogr;(√&psgr;*) = &Ogr;(n3/8) for the more restricted case of graphs with girth at least 6, due to Krista and Lorys [13].We also give the first hardness result for approximating the achromatic number. We show that for every fixed ∈ 0 there in no 2 - ∈ approximation algorithm, unless P = NP.