, Volume 41, Issue 4, pp 289–308 | Cite as

Inserting an Edge into a Planar Graph

  • Carsten GutwengerEmail author
  • Petra MutzelEmail author
  • René WeiskircherEmail author


Computing a crossing minimum drawing of a given planar graph G augmented by an additional edge e where all crossings involve e, has been a long standing open problem in graph drawing. Alternatively, the problem can be stated as finding a combinatorial embedding of a planar graph G where the given edge e can be inserted with the minimum number of crossings. Many problems concerned with the optimization over the set of all combinatorial embeddings of a planar graph turned out to be NP-hard. Surprisingly, we found a conceptually simple linear time algorithm based on SPQR-trees, that is able to find a solution with the minimum number of crossings.

Crossing minimization Combinatorial embeddings Planarization Graph drawing 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Research Center caesar, Ludwig-Erhard-Allee 2, D-53175 BonnGermany
  2. 2.Vienna University of Technology, Favoritenstrasse 9–11 E186, A-1040 ViennaAustria

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