### 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≤i≤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].

Original language | English (US) |
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Pages (from-to) | 361-373 |

Number of pages | 13 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*SIAM Journal on Discrete Mathematics*, vol. 21, no. 2, pp. 361-373. https://doi.org/10.1137/S0895480104442947

**An improved approximation of the achromatic number on bipartite graphs.** / Kortsarz, Guy; Shende, Sunil.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Kortsarz, Guy

AU - Shende, Sunil

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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].

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].

UR - http://www.scopus.com/inward/record.url?scp=45249092315&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45249092315&partnerID=8YFLogxK

U2 - 10.1137/S0895480104442947

DO - 10.1137/S0895480104442947

M3 - Article

AN - SCOPUS:45249092315

VL - 21

SP - 361

EP - 373

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -