Points and triangles in the plane and halving planes in space
Discrete & Computational Geometry
Improved bounds for intersecting triangles and halving planes
Journal of Combinatorial Theory Series A
The colored Tverberg's problem and complexes of injective functions
Journal of Combinatorial Theory Series A
Lectures on Discrete Geometry
Lower bounds for weak epsilon-nets and stair-convexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
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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 @W(m^3/(n^6log^2n)) triangles of T. Eppstein [D. Eppstein, Improved bounds for intersecting triangles and halving planes, J. Combin. Theory Ser. A 62 (1993) 176-182] 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.