Eppstein's bound on intersecting triangles revisited

摘要

Let S be a set of it points in the plane, and let T be a set of in 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 [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. (C) 2008 Elsevier Inc. All rights reserved.