Finding Convex Sets in Convex Position

denote a family of pairwise disjoint convex sets in the plane. is said to be in convex position, if none of its members is contained in the convex hull of the union of the others. For any fixed , we give a linear upper bound on , the maximum size of a family with the property that any k members of are in convex position, but no n are.

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Received January 12, 1998

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Tóth, G. Finding Convex Sets in Convex Position. Combinatorica 20, 589–596 (2000). https://doi.org/10.1007/s004930070010

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  • AMS Subject Classification (1991) Classes:  52C10