Name
Abstract | ||
|---|---|---|
Let P be a finite point set in the plane. A 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 Erdős, 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|). |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.comgeo.2017.07.002 | Computational Geometry |
Keywords | Field | DocType |
Dirac–Motzkin Conjecture,Incidences,Ordinary lines,Ordinary triangle,Planar point set | Discrete mathematics,Combinatorics,Triangle group,Existential quantification,Integer triangle,Point set,Mathematics | Journal |
Volume | ISSN | Citations |
66 | 0925-7721 | 0 |
PageRank | References | Authors |
0.34 | 3 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Radoslav Fulek | 1 | 125 | 22.27 |
| Hossein Nassajian Mojarrad | 2 | 0 | 0.34 |
| Marton Naszodi | 3 | 21 | 7.87 |
| Jozsef Solymosi | 4 | 22 | 5.10 |
| Sebastian U. Stich | 5 | 135 | 16.54 |
| May Szedlák | 6 | 0 | 0.68 |