An extension of the Erdős-Szekeres theorem on large angles


The existence of a functionn(ε) (ε>0) is established such that given a finite setV in the plane there exists a subsetWV, |W|<n(ε) with the property that for anyv εV\ W there are two pointsw 1,w 2 εW such that the angle ∢(w 1 vw 2)>π-ε.

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Bárány, I. An extension of the Erdős-Szekeres theorem on large angles. Combinatorica 7, 161–169 (1987).

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AMS subject classification (1980)

  • 51 M 05