On the existence of ordinary triangles
Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. 2017. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 66, 28–31.
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| Published
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Author
Fulek, RadoslavISTA 
;
Mojarrad, Hossein;
Naszódi, Márton;
Solymosi, József;
Stich, Sebastian;
Szedlák, May
;
Mojarrad, Hossein;
Naszódi, Márton;
Solymosi, József;
Stich, Sebastian;
Szedlák, MayDepartment
Abstract
Let P be a finite point set in the plane. A cordinary 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 Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c > 0such 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 |).
Publishing Year
Date Published
2017-01-01
Journal Title
Computational Geometry: Theory and Applications
Volume
66
Page
28 - 31
ISSN
IST-REx-ID
Cite this
Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 2017;66:28-31. doi:10.1016/j.comgeo.2017.07.002
Fulek, R., Mojarrad, H., Naszódi, M., Solymosi, J., Stich, S., & Szedlák, M. (2017). On the existence of ordinary triangles. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.07.002
Fulek, Radoslav, Hossein Mojarrad, Márton Naszódi, József Solymosi, Sebastian Stich, and May Szedlák. “On the Existence of Ordinary Triangles.” Computational Geometry: Theory and Applications. Elsevier, 2017. https://doi.org/10.1016/j.comgeo.2017.07.002.
R. Fulek, H. Mojarrad, M. Naszódi, J. Solymosi, S. Stich, and M. Szedlák, “On the existence of ordinary triangles,” Computational Geometry: Theory and Applications, vol. 66. Elsevier, pp. 28–31, 2017.
Fulek R, Mojarrad H, Naszódi M, Solymosi J, Stich S, Szedlák M. 2017. On the existence of ordinary triangles. Computational Geometry: Theory and Applications. 66, 28–31.
Fulek, Radoslav, et al. “On the Existence of Ordinary Triangles.” Computational Geometry: Theory and Applications, vol. 66, Elsevier, 2017, pp. 28–31, doi:10.1016/j.comgeo.2017.07.002.
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