Erdős–Szekeres theorem with forbidden order types

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Abstract

According to the classical Erdős–Szekeres theorem, every sufficiently large set of points in general position in the plane contains a large subset in convex position. Parallel to the Erdős–Hajnal problem in graph-Ramsey theory, we investigate how large such subsets must a configuration contain if it does not have any sub-configuration belonging to a fixed order type.

Keywords

Erdős–Szekeres theorem
Order type
Ramsey theory
Erdős–Szekeres conjecture
Combinatorial convexity

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Visiting the Rényi Institute of the Hungarian Academy of Sciences.