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

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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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/n≤ p ≤ 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.

Research supported by the Deutsche Forschungsgemeinschaft (DFG FOR 413/1-1)

Supported by NSF PHY-0071139 and Los Alamos National Laboratory.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Amin Coja-Oghlan

  2. University of New Mexico, Albuquerque, NM, 87131

    Cristopher Moore & Vishal Sanwalani

Authors
  1. Amin Coja-Oghlan
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  2. Cristopher Moore
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  3. Vishal Sanwalani
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Coja-Oghlan, A., Moore, C., Sanwalani, V. (2003). MAX k-CUT and Approximating the Chromatic Number of Random Graphs. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_18

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  • DOI: https://doi.org/10.1007/3-540-45061-0_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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