Improvement on the Decay of Crossing Numbers

  • Jakub Černý
  • Jan Kynčl
  • Géza Tóth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4875)


We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε> 0 there is a δ> 0 such that for n sufficiently large, every graph G with n vertices and m ≥ n 1 + ε edges has a subgraph G′ of at most (1 − δ)m edges and crossing number at least Open image in new window . This generalizes the result of J. Fox and Cs. Tóth.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jakub Černý
    • 1
  • Jan Kynčl
    • 1
  • Géza Tóth
    • 2
  1. 1.Department of Applied Mathematics, Faculty of Mathematics and PhysicsCharles UniversityCzech Republic
  2. 2.Hungarian Academy of SciencesRényi InstituteBudapestHungary

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