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Uncover Low Degree Vertices and Minimise the Mess: Independent Sets in Random Regular Graphs

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Mathematical Foundations of Computer Science 2007 (MFCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4708))

Abstract

We present algorithmic lower bounds on the size s d of the largest independent sets of vertices in random d-regular graphs, for each fixed d ≥ 3. For instance, for d = 3 we prove that, for graphs on n vertices, s d  ≥ 0.43475 n with probability approaching one as n tends to infinity.

Part of this work was carried out during a visit of the second author to the Australian National University (ANU). The authors wish to thank the Mathematical Sciences Institute at the ANU for its support.

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Author information

Authors and Affiliations

  1. Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia

    William Duckworth

  2. Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK

    Michele Zito

Authors
  1. William Duckworth
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  2. Michele Zito
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Luděk Kučera Antonín Kučera

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© 2007 Springer-Verlag Berlin Heidelberg

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Duckworth, W., Zito, M. (2007). Uncover Low Degree Vertices and Minimise the Mess: Independent Sets in Random Regular Graphs. In: Kučera, L., Kučera, A. (eds) Mathematical Foundations of Computer Science 2007. MFCS 2007. Lecture Notes in Computer Science, vol 4708. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74456-6_7

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  • DOI: https://doi.org/10.1007/978-3-540-74456-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74455-9

  • Online ISBN: 978-3-540-74456-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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