Geometriae Dedicata

, Volume 31, Issue 1, pp 89–104

Nine convex sets determine a pentagon with convex sets as vertices

  • T. Bisztriczky
  • G. Fejes Tóth

DOI: 10.1007/BF00184161

Cite this article as:
Bisztriczky, T. & Tóth, G.F. Geom Dedicata (1989) 31: 89. doi:10.1007/BF00184161


It is proved that if ℱ is a family of nine pairwise disjoint compact convex sets in the plane such that no member of ℱ is contained in the convex hull of the union of two other sets of ℱ, then ℱ has a subfamily ℱ′ with five elements such that no member of ℱ′ is contained in the convex hull of the union of the other sets of ℱ′.

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

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

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