Graphs drawn with few crossings per edge

  • János Pach
  • Géza Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)


We show that if a graph of v vertices can be drawn in the plane so that every edge crosses at most k> 0 others, then its number of edges cannot exceed 4.108√kv. For k≤ 4, we establish a better bound, (k + 3)(u− 2), which is tight for k=1 and 2. We apply these estimates to improve a result of Ajtai et al. and Leighton, providing a general lower bound for the crossing number of a graph in terms of its number of vertices and edges.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • János Pach
    • 1
  • Géza Tóth
    • 1
  1. 1.Courant InstituteNew York UniversityNew York

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