Simultaneous Embedding of Planar Graphs with Few Bends

  • Cesim Erten
  • Stephen G. Kobourov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)


We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n 2O(n 2) grid, with at most three bends per edge, where n is the number of vertices. For the case when the input graphs are both trees, only one bend per edge is required. We also describe an O(n) time algorithm for simultaneous embedding with fixed-edges for tree-path pairs on the O(nO(n 2) grid with at most one bend per tree-edge and no bends along path edges.


Planar Graph Hamiltonian Cycle Input Graph Planar Embedding Geometric Thickness 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cesim Erten
    • 1
  • Stephen G. Kobourov
    • 1
  1. 1.Department of Computer ScienceUniversity of Arizona 

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