Eppstein's bound on intersecting triangles revisited

Details Eppstein's bound on intersecting triangles revisited Eppstein's bound on intersecting triangles revisited

2008-04-28

arxiv.org/abs/0804.4415v2

Computer Science

Computational Geometry

Minor revision following referee's suggestions. To appear in Journal of Combinatorial Theory, Series A. 5 pages, 1 figure

Scientific paper

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.

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