Fulek, RadoslavMojarrad, Hossein NassajianNaszódi, MártonSolymosi, JózsefStich, Sebastian U.Szedlák, May2017-08-022017-08-022017-08-02201710.1016/j.comgeo.2017.07.002https://infoscience.epfl.ch/handle/20.500.14299/139521Let 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|).Dirac–Motzkin ConjectureIncidencesOrdinary linesOrdinary trianglePlanar point settext::journal::journal article::research article