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On Retracts, Absolute Retracts, and Folds in Cographs

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Graph-Theoretic Concepts in Computer Science (WG 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8165))

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Abstract

Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NP-complete. We show that this problem is fixed-parameter tractable when parameterized by the order of H. When restricted to the class of threshold graphs or to the class of trivially perfect graphs, the problem becomes tractable in polynomial time. The problem is also solvable in linear time when one cograph is given as an induced subgraph of the other. We characterize absolute retracts for the class of cographs. Foldings generalize retractions. We show that the problem to fold a trivially perfect graph onto a largest possible clique is NP-complete. For a threshold graph this folding number equals its chromatic number and achromatic number.

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Author information

Authors and Affiliations

  1. Department of Computer Science, National Tsing Hua University, Taiwan

    Ton Kloks

  2. Department of Information Management, National Taiwan University of Science and Technology, Taiwan

    Yue-Li Wang

Authors
  1. Ton Kloks
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  2. Yue-Li Wang
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Rostock, Albert-Einstein-Straße 22, 18059, Rostock, Germany

    Andreas Brandstädt

  2. Department of Computer Science, University of Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Institute of Theoretical Computer Science, University of Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Rüdiger Reischuk

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Kloks, T., Wang, YL. (2013). On Retracts, Absolute Retracts, and Folds in Cographs. In: Brandstädt, A., Jansen, K., Reischuk, R. (eds) Graph-Theoretic Concepts in Computer Science. WG 2013. Lecture Notes in Computer Science, vol 8165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45043-3_28

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  • DOI: https://doi.org/10.1007/978-3-642-45043-3_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45042-6

  • Online ISBN: 978-3-642-45043-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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