# An improved approximation of the achromatic number on bipartite graphs

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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 {Vi}1≤i≤k such that for every distinct pair of subsets Vi, Vj 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(n4/5) 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].

Original language English (US) 361-373 13 SIAM Journal on Discrete Mathematics 21 2 https://doi.org/10.1137/S0895480104442947 Published - Dec 1 2007

### Fingerprint

Achromatic number
Bipartite Graph
Subset
Approximation
Greedy Algorithm
Best Approximation
Partition
Distinct
Graph in graph theory

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### Cite this

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title = "An improved approximation of the achromatic number on bipartite graphs",
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 {Vi}1≤i≤k such that for every distinct pair of subsets Vi, Vj 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(n4/5) 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].",
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In: SIAM Journal on Discrete Mathematics, Vol. 21, No. 2, 01.12.2007, p. 361-373.

Research output: Contribution to journalArticle

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T1 - An improved approximation of the achromatic number on bipartite graphs

AU - Kortsarz, Guy

AU - Shende, Sunil

PY - 2007/12/1

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AB - 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 {Vi}1≤i≤k such that for every distinct pair of subsets Vi, Vj 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(n4/5) 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].

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