Eppstein's bound on intersecting triangles revisited
Computational Geometry
2013-03-25 v2
Abstract
Let S be a set of n points in the plane, and let T be a set of m triangles with vertices in S. Then there exists a point in the plane contained in Omega(m^3 / (n^6 log^2 n)) triangles of T. Eppstein (1993) gave a proof of this claim, but there is a problem with his proof. Here we provide a correct proof by slightly modifying Eppstein's argument.
Cite
@article{arxiv.0804.4415,
title = {Eppstein's bound on intersecting triangles revisited},
author = {Gabriel Nivasch and Micha Sharir},
journal= {arXiv preprint arXiv:0804.4415},
year = {2013}
}
Comments
Minor revision following referee's suggestions. To appear in Journal of Combinatorial Theory, Series A. 5 pages, 1 figure