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Improved Hardness of Approximating Chromatic Number

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2013, RANDOM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8096))

Abstract

We prove that for sufficiently large K, it is NP-hard to color K-colorable graphs with less than \(2^{\Omega(K^{1/3})}\) colors. This improves the previous result of K versus \(K^{\frac{1}{25}\log K}\) in Khot [1].

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Author information

Authors and Affiliations

  1. KTH Royal Institute of Technology, Stockholm, Sweden

    Sangxia Huang

Authors
  1. Sangxia Huang
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Editor information

Editors and Affiliations

  1. University of California, Berkeley, CA, USA

    Prasad Raghavendra

  2. Dept. of computer Science and Engineering, Pennsylvania State University, University Park, PA, USA

    Sofya Raskhodnikova

  3. Institute of Computer Science, University of Kiel, 24118, Kiel, Germany

    Klaus Jansen

  4. University of Geneva, Centre Universitaire d’Informatique, 1227, Carouge, Switzerland

    José D. P. Rolim

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Huang, S. (2013). Improved Hardness of Approximating Chromatic Number. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2013 2013. Lecture Notes in Computer Science, vol 8096. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40328-6_17

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  • DOI: https://doi.org/10.1007/978-3-642-40328-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40327-9

  • Online ISBN: 978-3-642-40328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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