Geometric Graphs with No Self-intersecting Path of Length Three

  • János Pach
  • Rom Pinchasi
  • Gábor Tardos
  • Géza Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)


Let G be a geometric graph with n vertices, i.e., a graph drawn in the plane with straight-line edges. It is shown that if G has no self-intersecting path of length 3, then its number of edges is O(n log n). This result is asymptotically tight. Analogous questions for curvilinear drawings and for longer paths are also considered.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • János Pach
    • 1
  • Rom Pinchasi
    • 2
  • Gábor Tardos
    • 3
  • Géza Tóth
    • 4
  1. 1.City College, CUNY and Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Rényi Institute of the Hungarian Academy of SciencesHungary
  4. 4.Rényi Institute of the Hungarian Academy of SciencesHungary

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