Eppstein's bound on intersecting triangles revisited
arXiv:0804.4415 · doi:10.1016/j.jcta.2008.07.003
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.
Minor revision following referee's suggestions. To appear in Journal of Combinatorial Theory, Series A. 5 pages, 1 figure