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arXiv · 0804.4415

Eppstein's bound on intersecting triangles revisited

Gabriel Nivasch·Micha Sharir
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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.

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Gabriel Nivasch, Micha Sharir. 2008-04-28. Eppstein's bound on intersecting triangles revisited. https://doi.org/10.1016/j.jcta.2008.07.003

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