Disjoint edges in geometric graphs


Answering an old question in combinatorial geometry, we show that any configuration consisting of a setV ofn points in general position in the plane and a set of 6n − 5 closed straight line segments whose endpoints lie inV, contains three pairwise disjoint line segments.


  1. [AA]

    J. Akiyama and N. Alon, Disjoint simplices and geometric hypergraphs,Proc. 3rd New York Conference on Combinatorial Mathematics, Annals of the New York Academy of Sciences, to appear.

  2. [AH]

    S. Avital and H. Hanani, Graphs,Gilyonot Lematematika 3(2) (1966), 2–8 (in Hebrew).

    Google Scholar 

  3. [Er]

    P. Erdös, On sets of distances ofn points,Amer. Math. Monthly 53 (1946), 248–250.

    MathSciNet  Article  MATH  Google Scholar 

  4. [Ku]

    Y. S. Kupitz,Extremal Problems in Combinatorial Geometry, Aarhus University Lecture Notes Series, No. 53, Aarhus University, Denmark, 1979.

    Google Scholar 

  5. [Pe]

    M. A. Perles, Unpublished notes.

Download references

Author information



Additional information

Research supported in part by an Allon Fellowship and by a Bat Sheva de-Rothschild grant.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Alon, N., Erdös, P. Disjoint edges in geometric graphs. Discrete Comput Geom 4, 287–290 (1989). https://doi.org/10.1007/BF02187731

Download citation


  • General Position
  • Pairwise Disjoint
  • Discrete Comput Geom
  • Straight Line Segment
  • Geometric Graph