Crossing families
Boris S. Aronov, Paul L. Erdos, Wayne Goddard, Daniel J. Kleitman, Michael Klugerman, János Pach, Leonard J. Schulman · 1991
Given n points in the plane, a crossing family is a collection of line segments, each joining two of the points, such that any two line segments intersect internally.We show that any n points in general position possess a crossing family of size at least ~, and describe an O(n log n)-time algorithm for finding one.