How Many Ways Can One Draw a Graph?

  • János Pach
  • Géza Tóth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)

Abstract

Using results from extremal graph theory, we determine the asymptotic number of string graphs with n vertices, i.e., graphs that can be obtained as the intersection graph of a system of continuous arcs in the plane. The number becomes much smaller, for any fixed d, if we restrict our attention to systems of arcs, any two of which cross at most d times. As an application, we estimate the number of different drawings of the complete graph K n with n vertices under various side conditions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • János Pach
    • 1
  • Géza Tóth
    • 1
  1. 1.Rényi InstituteHungarian Academy of SciencesBudapestHungary

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