Disjoint edges in geometric graphs

Abstract

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.

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

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

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Keywords

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