Let
g(n) denote the least value such that any
g(n) points in the plane in general position contain the vertices of a convex
n -gon. In 1935, Erdős and Szekeres showed that
g(n) exists, and they obtained the bounds
Chung and Graham have recently improved the upper bound by 1; the first improvement since the original Erdős—Szekeres paper.
We show that
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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;
<pdfname>19n3p405.pdf
<pdfexist>yes
<htmlexist>no
<htmlfexist>no
<texexist>yes
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Received January 1, 1997, and in revised form June 6, 1997.