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An Improved Approximation of the Achromatic Number on Bipartite Graphs
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An Improved Approximation of the Achromatic Number on Bipartite Graphs
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Journal Article
An Improved Approximation of the Achromatic Number on Bipartite Graphs
2007
Overview
The achromatic number of a graph$G = (V,E)$with$|V| = n$vertices is the largest number$k$with the following property: the vertices of$G$can be partitioned into$k$independent subsets$\\{V_i\\}_{1 \\leq i \\leq k}$such that for every distinct pair of subsets$V_i,V_j$in the partition, there is at least one edge in$E$that connects these subsets. We describe a greedy algorithm that computes the achromatic number of a bipartite graph within a factor of$O(n^{4/5})$of the optimal. Prior to our work, the best known approximation factor for this problem was$n \\log\\log n /\\log n$as shown by Kortsarz and Krauthgamer [SIAM J. Discrete Math., 14 (2001), pp. 408-422].
Publisher
Society for Industrial and Applied Mathematics
Subject
