Discrete & Computational Geometry

, Volume 7, Issue 2, pp 109–123

An upper bound on the number of planarK-sets

  • János Pach
  • William Steiger
  • Endre Szemerédi
Article

DOI: 10.1007/BF02187829

Cite this article as:
Pach, J., Steiger, W. & Szemerédi, E. Discrete Comput Geom (1992) 7: 109. doi:10.1007/BF02187829

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.

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