Discrete & Computational Geometry

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

Empty Convex Hexagons in Planar Point Sets

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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