Forced Convex n -Gons in the Plane

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1998 English Publisher:Springer Science and Business Media LLCJournal:Discrete & Computational Geometry, volume 19, pages 367-371 (issn: 0179-5376,

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Authors: Fan R. K. Chung; Ronald L. Graham;

doi: 10.1007/pl00009353

Forced Convex n -Gons in the Plane

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Abstract

Denote by \(g(n)\) the smallest number such that every set of \(g(n)\) points in the plane in general position contains the vertices of a convex \(n\)-gon. In 1935 Erdős and Szekeres proved that \[ 2^{n- 2}+ 1\leq g(n)\leq {2n-4\choose n-2}+ 1. \] The authors of the present paper lessen the right estimate by 1.

Related Organizations

University of Pennsylvania
United States

Keywords

vertex, Convex sets in \(2\) dimensions (including convex curves), convex \(n\)-gon, Erdős problems and related topics of discrete geometry

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