Upward drawings on planes and spheres

Extended abstract for Graph Drawing '95 20 – 22 September 1995
  • S. Mehdi Hashemi
  • Andrzej Kisielewicz
  • Ivan Rival
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)


Although there is a linear time algorithm to decide whether an ordered set has an upward drawing on a surface topologically equivalent to a sphere, we shall prove that the decision problem whether an ordered set has an upward drawing on a sphere itself is NP-complete. To this end we explore the surface topology of ordered sets highlighting especially the role of their saddle points.


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • S. Mehdi Hashemi
    • 1
  • Andrzej Kisielewicz
    • 2
  • Ivan Rival
    • 3
  1. 1.Department of MathematicsUniversity of OttawaOttawaCanada
  2. 2.Mathematical InstituteUniversity of WroclawWroclawPoland
  3. 3.Department of Computer ScienceUniversity of OttawaOttawaCanada

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