Crossing Families

11 years 11 months ago
Crossing Families
Given a set of 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. Two sets A and B of points in the plane are mutually avoiding if no line subtended by a pair of points in A intersects the convex hull of B, and vice versa. We show that any set of n points in general position contains a pair of mutually avoiding subsets each of size at least n/12. As a consequence we show that such a set possesses a crossing family of size at least n/12, and describe a fast algorithm for finding such a family. AMS classification: 52C10; also 68Q20
Boris Aronov, Paul Erdös, Wayne Goddard, Dani
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Authors Boris Aronov, Paul Erdös, Wayne Goddard, Daniel J. Kleitman, Michael Klugerman, János Pach, Leonard J. Schulman
Comments (0)