On approximating the achromatic number

Guy Kortsarz, Robert Krauthgamer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The achromatic number problem is to legally color the vertices of an input graph with the maximum number of colors, denoted &psgr;*, so that every two color classes share at least one edge. This problem is known to be NP-hard. For general graphs we give an algorithm that approximates the achromatic number within ratio of &Ogr;(n -log log n/ log n). This improves over the previously known approximation ratio of &Ogr; (n/Vlog n), due to Chaudhary and Vishwanathan [4]. For graphs of girth at least 5 we give an algorithm with approximation ratio &Ogr;(min{n1/3, V&psgr;*}). This improves over an approximation ratio &Ogr;(V&psgr;*) = &Ogr;(n3/8) for the more restricted case of graphs with girth at least 6, due to Krista and Lorys [13]. We also give the first hardness result for approximating the achromatic number. We show that for every fixed □ > 0 there in no 2 - D approximation algorithm, unless P = NP.

Original languageEnglish
Title of host publicationProceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms
Number of pages10
StatePublished - 2001
Event2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States
Duration: 30 Apr 20011 May 2001

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference2001 Operating Section Proceedings, American Gas Association
Country/TerritoryUnited States
CityDallas, TX


  • Algorithms
  • Theory
  • Verification


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