Spherical-Rectangular Drawings

  • Mahdieh Hasheminezhad
  • S. Mehdi Hashemi
  • Brendan D. McKay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5431)


We extend the concept of rectangular drawing to drawings on a sphere using meridians and circles of latitude such that each face is bounded by at most two circles and at most two meridians. This is called spherical-rectangular drawing. Special cases include drawing on a cylinder, a cone, or a lattice of concentric circles on the plane. In this paper, we prove necessary and sufficient conditions for cubic planar graphs to have spherical-rectangular drawings, and show that one can find in linear time a spherical-rectangular drawing of a subcubic planar graph if it has one.


Plane Graph Linear Time Concentric Circle Parallel Edge External Face 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mahdieh Hasheminezhad
    • 1
  • S. Mehdi Hashemi
    • 1
  • Brendan D. McKay
    • 2
  1. 1.Department of Computer Science, Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran
  2. 2.Department of Computer ScienceAustralian National UniversityCanberraAustralia

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