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Acta Mathematica Hungarica

, Volume 157, Issue 2, pp 301–311 | Cite as

On crossing families of complete geometric graphs

  • D. Lara
  • C. Rubio-MontielEmail author
Article

Abstract

A crossing family is a collection of pairwise crossing segments, this concept was introduced by Aronov et al. [4]. They proved 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.

Key words and phrases

combinatorial geometry intersecting families Erdős–Szekeres theorem 

Mathematics Subject Classification

52C10 68R10 05C12 

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Notes

Acknowledgement

The authors thank the referee for helpful advice on an earlier draft of the paper.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Departamento de ComputaciónCentro de Investigación y de Estudios Avanzados del Instituto Politécnico NacionalNaucalpanMexico
  2. 2.División de Matemáticas e Ingeniería, FES AcatlánUniversidad Nacional Autónoma de MéxicoNaucalpanMexico

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