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Eppstein’s bound on intersecting triangles revisited. (English)
J. Comb. Theory, Ser. A 116, No. 2, 494-497 (2009).
Summary: 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 $\varOmega (m^{3}/(n^{6}\log ^{2}n))$ triangles of $T$. {\it D. Eppstein} [J. Comb. Theory, Ser. A 62, No.~1, 176‒182 (1993; Zbl 0769.68122)] 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.