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Finding a Maximum Induced Degenerate Subgraph Faster Than 2n

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Parameterized and Exact Computation (IPEC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7535))

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Abstract

In this paper we study the problem of finding a maximum induced d-degenerate subgraph in a given n-vertex graph from the point of view of exact algorithms. We show that for any fixed d one can find a maximum induced d-degenerate subgraph in randomized \((2-\varepsilon _d)^nn^{\mathcal{O}(1)}\) time, for some constant ε d  > 0 depending only on d. Moreover, our algorithm can be used to sample inclusion-wise maximal induced d-degenerate subgraphs in such a manner that every such subgraph is output with probability at least (2 − ε d )− n; hence, we prove that their number is bounded by (2 − ε d )n.

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Author information

Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Poland

    Marcin Pilipczuk

  2. Department of Informatics, University of Bergen, Norway

    Michał Pilipczuk

Authors
  1. Marcin Pilipczuk
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  2. Michał Pilipczuk
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National and Kapodistrian University of Athens, Panepistimioupolis, 15784, Athens, Greece

    Dimitrios M. Thilikos

  2. Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Pilipczuk, M., Pilipczuk, M. (2012). Finding a Maximum Induced Degenerate Subgraph Faster Than 2n . In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-33293-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33292-0

  • Online ISBN: 978-3-642-33293-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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