On crossing families of complete geometric graphs

Abstract

A crossing family is a collection of pairwise crossing segments, this concept was introduced by Aronov et. al. (1994). They prove that any set of $n$ points (in general position) in the plain contains a crossing family of size $\sqrt{n/12}$. In this paper we present a generalization of the concept and give several results regarding this generalization.

arXiv comment23 pages, 16 figures