1. On crossing families of complete geometric graphs
- Author
-
Christian Rubio-Montiel and Dolores Lara
- Subjects
05C10, 68R10 ,Generalization ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Combinatorics ,Set (abstract data type) ,FOS: Mathematics ,Mathematics - Combinatorics ,Pairwise comparison ,Combinatorics (math.CO) ,0101 mathematics ,General position ,Mathematics - 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., 23 pages, 16 figures
- Published
- 2018