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Planar point sets determine many pairwise crossing segments
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-06-08 , DOI: 10.1016/j.aim.2021.107779 János Pach , Natan Rubin , Gábor Tardos
中文翻译:
平面点集确定许多成对的交叉线段
更新日期:2021-06-08
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-06-08 , DOI: 10.1016/j.aim.2021.107779 János Pach , Natan Rubin , Gábor Tardos
We show that any set of n points in general position in the plane determines pairwise crossing segments. The best previously known lower bound, , was proved more than 25 years ago by Aronov, Erdős, Goddard, Kleitman, Klugerman, Pach, and Schulman. Our proof is fully constructive, and extends to dense geometric graphs.
中文翻译:
平面点集确定许多成对的交叉线段
我们表明,平面中一般位置的任何一组n个点决定成对交叉段。以前已知的最好的下界,25 多年前,Aronov、Erdős、Goddard、Kleitman、Klugerman、Pach 和 Schulman 证明了这一点。我们的证明是完全建设性的,并扩展到密集的几何图形。