Nine convex sets determine a pentagon with convex sets as vertices |
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| Authors: | T Bisztriczky G Fejes Tóth |
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| Institution: | (1) Department of Mathematics and Statistics, University of Calgary, 2500 University Dr. N. W., T2N 1N4 Calgary, Alberta, Canada;(2) Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest, Hungary |
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| Abstract: | 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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