Discrete & Computational Geometry

, Volume 39, Issue 1, pp 239–272

Empty Convex Hexagons in Planar Point Sets


DOI: 10.1007/s00454-007-9018-x

Cite this article as:
Gerken, T. Discrete Comput Geom (2008) 39: 239. doi:10.1007/s00454-007-9018-x


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.


Erdős-Szekeres problemRamsey theoryConvex polygons and polyhedraEmpty hexagon problem

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Zentrum MathematikTechnische Universität MünchenGarchingGermany