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Empty Convex Hexagons in Planar Point Sets

By Tobias Gerken

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

Year: 2007
OAI identifier: oai:CiteSeerX.psu:10.1.1.135.1606
Provided by: CiteSeerX
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