Nine convex sets determine a pentagon with convex sets as vertices
- Cite this article as:
- Bisztriczky, T. & Tóth, G.F. Geom Dedicata (1989) 31: 89. doi:10.1007/BF00184161
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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′.