Achromatic number is NP-complete for cographs and interval graphs
Information Processing Letters
Approximating the minimum maximal independence number
Information Processing Letters
The complexity of harmonious colouring for trees
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Approximation algorithms for NP-hard problems
Some results on the achromatic number
Journal of Graph Theory
The achromatic number of bounded degree trees
Discrete Mathematics
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Balls and bins: a study in negative dependence
Random Structures & Algorithms
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Some optimal inapproximability results
Journal of the ACM (JACM)
On Approximating the Achromatic Number
SIAM Journal on Discrete Mathematics
Approximating the Domatic Number
SIAM Journal on Computing
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the pseudo-achromatic number problem
Theoretical Computer Science
On the Pseudo-achromatic Number Problem
Graph-Theoretic Concepts in Computer Science
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A complete partition of a graph G is a partition of V(G) such that any two classes are connected by an edge. Let cp(G) denote the maximum number of classes in a complete partition of G. This measure was defined in 1969 by Gupta [18], and is known to be NP-hard on several classes of graphs. We obtain the first, and essentially tight, lower and upper bounds on the approximability of this problem. We show that there is a randomized polynomial-time algorithm that given a graph G produces a complete partition of size Ω(cp(G)/√lg|V(G)|). This algorithm can be derandomized.We show that the upper bound is essentially tight: there is a constant C 1, such that if there is a randomized polynomial-time algorithm that for all large n, when given a graph G with n vertices produces a complete partition into at least C cp(G)/√lg n classes, then NP ⊆ RTime(no(lg lg n)). The problem of finding a complete partition of a graph is thus the first natural problem whose approximation threshold has been determined to be of the form θ((lg n)c) for some constant c strictly between 0 and 1.