Publication details
Triangles in arrangements of points and lines in the plane
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Combinatorial Theory, Series A |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.jcta.2010.11.002 |
| Keywords | Plane arrangements; Point-line incident graphs; Plane configurations |
| Description | A conjecture of de Caen and Szekely ID. de Caen, LA. Szekely, J. Combin. Theory Ser. A 77 (1997) 268-278] asserts that every arrangement of n points and m lines in the plane contains at most O(nm) triangles with vertices in the points and sides on the lines of the arrangement. We disprove the conjecture by constructing an arrangement of n points and n lines with Omega(n(2) log log n) such triangles. (C) 2010 Elsevier Inc. All rights reserved. |