arXiv 0804.44152008-04cs.CG

相交三角形上的Eppstein界

Eppstein's bound on intersecting triangles revisited

Gabriel Nivasch, Micha Sharir

备注：: Minor revision following referee's suggestions. To appear in Journal of Combinatorial Theory, Series A. 5 pages, 1 figure
发表信息：: Journal of Combinatorial Theory, Series A, 116:494-497, 2009
DOI：: 10.1016/j.jcta.2008.07.003

摘要：

设S是平面上n个点的集合，T是顶点在S中的m个三角形的集合。则在T的Ω（m^3 /（n^6 log^2 n））三角形所包含的平面上存在一点。Eppstein（1993）给出了一个证明，但他的证明有一个问题。在这里，我们提供了一个正确的证明略有修改Eppstein的论点。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。