Clustered Planarity Testing Revisited

  • Radoslav Fulek
  • Jan Kynčl
  • Igor Malinović
  • Dömötör Pálvölgyi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

Abstract

The Hanani–Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every pair of edges not sharing a vertex cross an even number of times. We generalize this classical result to clustered graphs with two disjoint clusters, and show that a straightforward extension of our result to flat clustered graphs with three or more disjoint clusters is not possible.

We also give a new and short proof for a related result by Di Battista and Frati based on the matroid intersection algorithm.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Radoslav Fulek
    • 1
    • 4
  • Jan Kynčl
    • 1
  • Igor Malinović
    • 2
  • Dömötör Pálvölgyi
    • 3
  1. 1.Department of Applied Mathematics and Institute for Theoretical Computer Science,Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic
  2. 2.Faculté Informatique et CommunicationsÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.Institute of MathematicsEötvös UniversityBudapestHungary
  4. 4.Department of Industrial Engineering and Operations ResearchColumbia UniversityNew York CityUSA

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