On the Number of Upward Planar Orientations of Maximal Planar Graphs

  • Fabrizio Frati
  • Joachim Gudmundsson
  • Emo Welzl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)


We consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have. We show that n-vertex maximal planar graphs have at least Ω(n ·1.189 n ) and at most O(n ·4 n ) upward planar orientations. Moreover, there exist n-vertex maximal planar graphs having as few as O(n ·2 n ) upward planar orientations and n-vertex maximal planar graphs having Ω(2.599 n ) upward planar orientations.


Directed Graph Planar Graph Internal Vertex Outer Face Internal Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fabrizio Frati
    • 1
  • Joachim Gudmundsson
    • 1
  • Emo Welzl
    • 2
  1. 1.School of Information TechnologiesThe University of SydneyAustralia
  2. 2.Institute of Theoretical Computer ScienceETH ZurichSwitzerland

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