Testing Simultaneous Planarity When the Common Graph Is 2-Connected

  • Bernhard Haeupler
  • Krishnam Raju Jampani
  • Anna Lubiw
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6507)

Abstract

Two planar graphs G1 and G2 sharing some vertices and edges are simultaneously planar if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a linear-time algorithm to test simultaneous planarity when the two graphs share a 2-connected subgraph. Our algorithm extends to the case of k planar graphs where each vertex [edge] is either common to all graphs or belongs to exactly one of them.

Keywords

Simultaneous Embedding Planar Graph PQ Tree Graph Drawing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bernhard Haeupler
    • 1
  • Krishnam Raju Jampani
    • 2
  • Anna Lubiw
    • 2
  1. 1.CSAIL, Dept. of Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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