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MAX k-CUT and Approximating the Chromatic Number of Random Graphs

  • Amin Coja-Oghlan
  • Cristopher Moore
  • Vishal Sanwalani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)

Abstract

We consider the MAX k-CUT problem in random graphs G n,p. First, we estimate the probable weight of a MAX k-CUT using probabilistic counting arguments and by analyzing a simple greedy heuristic. Then, we give an algorithm that approximates MAX k-CUT within expected polynomial time. The approximation ratio tends to 1 as np→ ∞. As an application, we obtain an algorithm for approximating the chromatic number of G n,p, 1/np ≤ 1/2, within a factor of \( O\left( {\sqrt {np} } \right) \) in polynomial expected time, thereby answering a question of Krivelevich and Vu, and extending a result of Coja-Oghlan and Taraz. We give similar algorithms for random regular graphs G n,r.

Keywords

Adjacency Matrix Random Graph Approximation Ratio Chromatic Number Graph Coloring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Amin Coja-Oghlan
    • 1
  • Cristopher Moore
    • 2
  • Vishal Sanwalani
    • 2
  1. 1.Institut für InformatikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.University of New MexicoAlbuquerque

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