, Volume 19, Issue 3, pp 405-410

Finding Convex Sets Among Points in the Plane

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 \(2^{n-2}+1 \leq g(n) \leq {{2n-4} \choose {n-2}} +1. \) Chung and Graham have recently improved the upper bound by 1; the first improvement since the original Erdős—Szekeres paper. We show that \(g(n) \leq {{2n-4} \choose {n-2}}+7-2n.\) 26 June, 1998 Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; 19n3p405.pdf yes no no yes

Received January 1, 1997, and in revised form June 6, 1997.