An upper bound on the number of planar K-sets

János Pach, William Steiger, Endre Szemerédi

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Given a set S of n points, a subset X of size k is called a k-set if there is a hyperplane Π that separates X from S-X. We prove that O(n√k/log*k) is an upper bound for the number of k-sets in the plane, thus improving the previous bound of Erdös, Lovász, Simmons, and Strauss by a factor of log*k.

Original languageEnglish
Pages (from-to)109-123
Number of pages15
JournalDiscrete & Computational Geometry
Volume7
Issue number1
DOIs
Publication statusPublished - Dec 1 1992

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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