The maximum size of a convex polygon in a restricted set of points in the plane

N. Alon, M. Katchalski, W. R. Pulleyblank

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Assume we have k points in general position in the plane such that the ratio between the maximum distance of any pair of points to the minimum distance of any pair of points is at most α√k, for some positive constant α. We show that there exist at least βk1/4 of these points which are the vertices of a convex polygon, for some positive constant β=β(α). On the other hand, we show that for every fixed ε>0, if k>k(ε), then there is a set of k points in the plane for which the above ratio is at most 4√k, which does not contain a convex polygon of more than k1/3+ε vertices.

Original languageEnglish (US)
Pages (from-to)245-251
Number of pages7
JournalDiscrete & Computational Geometry
Volume4
Issue number1
DOIs
StatePublished - Dec 1 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

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