Crossing patterns of segments

摘要

It is shown that for every c > 0 there exists c' > 0 satisfying the following condition. Let S be a system of n straight-line segments in the plane, which determine at least cn(2) crossings. Then there are two disjoint at least c'n-element subsystems, S-1,S- S-2 subset of S, such that every element of S-1 crosses all elements or S-2. (C) 2001 Academic Press. [References: 23]