Planar Crossing Numbers of Genus g Graphs

  • Hristo Djidjev
  • Imrich Vrt’o
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


Pach and Tóth [14] proved that any n-vertex graph of genus g and maximum degree d has a planar crossing number at most c g dn, for a constant c > 1. We improve on this results by decreasing the bound to O(dgn), if g = o(n), and to O(g 2), otherwise, and also prove that our result is tight within a constant factor.


Planar Graph Euler Characteristic Outer Face Simple Cycle Planar Crossing 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hristo Djidjev
    • 1
  • Imrich Vrt’o
    • 2
  1. 1.Los Alamos National LaboratoryLos AlamosUSA
  2. 2.Institute of MathematicsSlovak Academy of SciencesBratislavaSlovak Republic

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