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Discrete & Computational Geometry

, Volume 7, Issue 2, pp 109–123 | Cite as

An upper bound on the number of planarK-sets

  • János Pach
  • William Steiger
  • Endre Szemerédi
Article

Abstract

Given a setS ofn points, a subsetX of sizek is called ak-set if there is a hyperplane Π that separatesX fromS−X. We prove thatO(nk/log*k) is an upper bound for the number ofk-sets in the plane, thus improving the previous bound of Erdös, Lovász, Simmons, and Strauss by a factor of log*k.

Keywords

Angular Region Clockwise Order Irregular Edge Large Subgraph Intersection Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • János Pach
    • 1
    • 2
  • William Steiger
    • 3
  • Endre Szemerédi
    • 1
    • 3
  1. 1.Mathematical InstituteHungarian Academy of ScienceBudapestHungary
  2. 2.Courant InstituteNew York UniversityNew YorkUSA
  3. 3.Computer Science DepartmentRutgers UniversityNew BrunswickUSA

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