Forced Convex n -Gons in the Plane |
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Authors: | F R K Chung R L Graham |
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Affiliation: | (1) University of Pennsylvania, Philadelphia, PA 19104, USA chung@math.upenn.edu , US;(2) AT &T Labs—Research, Murray Hill, NJ 07974, USA, US |
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Abstract: | In a seminal paper from 1935, Erdős and Szekeres showed that for each n there exists a least value g(n) such that any subset of g(n) points in the plane in general position must always contain the vertices of a convex n -gon. In particular, they obtained the bounds which have stood unchanged since then. In this paper we remove the +1 from the upper bound for n ≥ 4 .
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<onlinepub>26 June, 1998
<editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt;
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Received January 1, 1997, and in revised form June 6, 1997. |
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