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A Note on Treewidth in Random Graphs

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6831))

Abstract

We show that in Erdős-Rényi random graph G(n,p) with high probability, when p = c/n and c is a constant, the treewidth is upper bounded by tn for some constant t < 1 which may depend on c, but when p ≫ 1/n, the treewidth is lower bounded by n − o(n). The upper bound refutes a conjecture that treewidth in G(n,p = c/n) is as large as n − o(n), and the lower bound provides further theoretical evidence on hardness of some random constraint satisfaction problems called Model RB and Model RD.

To whom the correspondence should be addressed: Tian Liu (lt@pku.edu.cn) and Ke Xu (kexu@nlsde.buaa.edu.cn).

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Author information

Authors and Affiliations

  1. Key Laboratory of Data Engineering and Knowledge Engineering, MOE, School of Information Resource Management, Renmin University of China, Beijing, 100872, P.R. China

    Chaoyi Wang & Tian Liu

  2. Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing, 100871, P.R. China

    Peng Cui

  3. National Lab of Software Development Environment, Beihang University, Beijing, 100083, P.R. China

    Ke Xu

Authors
  1. Chaoyi Wang
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  2. Tian Liu
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  3. Peng Cui
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  4. Ke Xu
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Editor information

Editors and Affiliations

  1. Zhejiang Normal University, 688 Yingbin Road, 321004, Jinhua, Zhejiang Province, China

    Weifan Wang  & Xuding Zhu  & 

  2. Department of Computer Science, University of Texas at Dallas, 75080, Richardson, TX, USA

    Ding-Zhu Du

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© 2011 Springer-Verlag Berlin Heidelberg

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Wang, C., Liu, T., Cui, P., Xu, K. (2011). A Note on Treewidth in Random Graphs. In: Wang, W., Zhu, X., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2011. Lecture Notes in Computer Science, vol 6831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22616-8_38

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  • DOI: https://doi.org/10.1007/978-3-642-22616-8_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22615-1

  • Online ISBN: 978-3-642-22616-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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