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Contractions of Planar Graphs in Polynomial Time

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Algorithms – ESA 2010 (ESA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6346))

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Abstract

We prove that for every graph H, there exists a polynomial-time algorithm deciding if a planar graph can be contracted to H. We introduce contractions and topological minors of embedded (plane) graphs and show that a plane graph H is an embedded contraction of a plane graph G, if and only if, the dual of H is an embedded topological minor of the dual of G. We show how to reduce finding embedded topological minors in plane graphs to solving an instance of the disjoint paths problem. Finally, we extend the result to graphs embeddable in an arbitrary surface.

This research was done while the two last authors were visiting the Département d’Informatique Université Libre de Bruxelles in January 2010.

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Author information

Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles,  

    Marcin Kamiński

  2. Department of Computer Science, University of Durham,  

    Daniël Paulusma

  3. Department of Mathematics, National and Kapodistrian University of Athens,  

    Dimitrios M. Thilikos

Authors
  1. Marcin Kamiński
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  2. Daniël Paulusma
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  3. Dimitrios M. Thilikos
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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Kamiński, M., Paulusma, D., Thilikos, D.M. (2010). Contractions of Planar Graphs in Polynomial Time. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_11

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  • DOI: https://doi.org/10.1007/978-3-642-15775-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15774-5

  • Online ISBN: 978-3-642-15775-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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