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On Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs

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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

Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a linear-time algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices of matrices that do not have the consecutive-ones property. We give a linear-time algorithm to find one in any matrix that does not have the consecutive-ones property.

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Author information

Authors and Affiliations

  1. Computer Science Department, Colorado State University, Fort Collins, CO, 80523-1873, U.S.A.

    Nathan Lindzey & Ross M. McConnell

Authors
  1. Nathan Lindzey
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  2. Ross M. McConnell
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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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© 2013 Springer-Verlag Berlin Heidelberg

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Lindzey, N., McConnell, R.M. (2013). On Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs. 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_30

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  • DOI: https://doi.org/10.1007/978-3-642-45043-3_30

  • 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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