1. Empty Convex Hexagons in Planar Point Sets
- Author
-
Tobias Gerken
- Subjects
Convex hull ,Convex analysis ,Convex set ,Subderivative ,Theoretical Computer Science ,Combinatorics ,Computational Theory and Mathematics ,Convex polytope ,Discrete Mathematics and Combinatorics ,Convex body ,Geometry and Topology ,Absolutely convex set ,Orthogonal convex hull ,Mathematics - Abstract
Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty convex hexagon.
- Published
- 2007
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