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- W2078903417 abstract "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 $n loglog n /log n$ as shown by Kortsarz and Krauthgamer [SIAM J. Discrete Math., 14 (2001), pp. 408–422]." @default.
- W2078903417 created "2016-06-24" @default.
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- W2078903417 date "2007-01-01" @default.
- W2078903417 modified "2023-09-25" @default.
- W2078903417 title "An Improved Approximation of the Achromatic Number on Bipartite Graphs" @default.
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- W2078903417 doi "https://doi.org/10.1137/s0895480104442947" @default.
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