Empty Convex Hexagons in Planar Point Sets
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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.
KeywordsErdős-Szekeres problem Ramsey theory Convex polygons and polyhedra Empty hexagon problem
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