On Simultaneous Planar Graph Embeddings

  • P. Brass
  • E. Cenek
  • C. A. Duncan
  • A. Efrat
  • C. Erten
  • D. Ismailescu
  • S. G. Kobourov
  • A. Lubiw
  • J. S. B. Mitchell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)


We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another in which the mapping is not given. In particular, given a mapping, we show how to embed two paths on an n ×n grid, and two caterpillar graphs on a 3n ×3n grid. We show that it is not always possible to simultaneously embed three paths. If the mapping is not given, we show that any number of outerplanar graphs can be embedded simultaneously on an O(n) ×O(n) grid, and an outerplanar and general planar graph can be embedded simultaneously on an O(n 2) ×O(n 2) grid.


Planar Graph Outerplanar Graph Convex Drawing Grid Drawing Related Graph Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • P. Brass
    • 1
  • E. Cenek
    • 2
  • C. A. Duncan
    • 3
  • A. Efrat
    • 4
  • C. Erten
    • 4
  • D. Ismailescu
    • 5
  • S. G. Kobourov
    • 4
  • A. Lubiw
    • 2
  • J. S. B. Mitchell
    • 6
  1. 1.Dept. of Computer ScienceCity College of New York 
  2. 2.Dept. of Computer ScienceUniversity of Waterloo 
  3. 3.Dept. of Computer ScienceUniv. of Miami 
  4. 4.Dept. of Computer ScienceUniv. of Arizona 
  5. 5.Dept. of MathematicsHofstra University 
  6. 6.Dept. of Applied Mathematics and StatisticsStony Brook University 

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