##
On the existence of ordinary triangles

Let P be a finite point set in the plane. A \emph{c-ordinary triangle} in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question of Erd\H{o}s, and answering a question of de Zeeuw, we prove that there exists a constant c>0 such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(|P|).

Published in:

Computational Geometry, 66, 28-31

Publisher:

Elsevier

ISSN:

0925-7721

Keywords:

Laboratories:

Record created 2017-08-02, last modified 2018-03-18