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Discrete & Computational Geometry

, Volume 39, Issue 1–3, pp 239–272 | Cite as

Empty Convex Hexagons in Planar Point Sets

  • Tobias Gerken
Article

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.

Keywords

Erdős-Szekeres problem Ramsey theory Convex polygons and polyhedra Empty hexagon problem 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenGarchingGermany

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