Combinatorica

, Volume 10, Issue 2, pp 195–202

Convexly independent sets

  • T. Bisztriczky
  • G. Fejes Tóth
Article

DOI: 10.1007/BF02123010

Cite this article as:
Bisztriczky, T. & Tóth, G.F. Combinatorica (1990) 10: 195. doi:10.1007/BF02123010

Abstract

A family of pairwise disjoint compact convex sets is called convexly independent, if none of its members is contained in the convex hull of the union of the other members of the family. The main result of the paper gives an upper bound for the maximum cardinalityh(k, n) of a family ℱ of mutually disjoint compact convex sets such that any subfamily of at mostk members of ℱ is convexly independent, but no subfamily of sizen is.

AMS subject classification (1980)

52 A 1005 A 17

Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • T. Bisztriczky
    • 1
  • G. Fejes Tóth
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCanada
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary