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.

This is a preview of subscription content, access via your institution.

Author information



Additional information

Received January 12, 1998

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tóth, G. Finding Convex Sets in Convex Position. Combinatorica 20, 589–596 (2000).

Download citation

  • AMS Subject Classification (1991) Classes:  52C10