Efficient Extraction of Multiple Kuratowski Subdivisions

  • Markus Chimani
  • Petra Mutzel
  • Jens M. Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for non-planarity. Modern planarity testing algorithms allow to extract a single such witness in linear time. We present the first linear time algorithm which is able to extract multiple Kuratowski subdivisions at once. This is of particular interest for, e.g., Branch-and-Cut algorithms which require multiple such subdivisions to generate cut constraints. The algorithm is not only described theoretically, but we also present an experimental study of its implementation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Markus Chimani
    • 1
  • Petra Mutzel
    • 1
  • Jens M. Schmidt
    • 1
  1. 1.Department of Computer ScienceUniversity of DortmundGermany

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