Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 59: Issue 3-4
Convex Polygons and Separation of Convex
Authors:
Eduardo Rivera-Campo Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa

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and
Jorge Urrutia Instituto de Matemáticas, Universidad Nacional Autónoma de México

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Pages:
274–283
Online Publication Date:
14 Dec 2022
Publication Date:
14 Dec 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2022.01530
Keywords:
Convex polygon; plane compact convex set; separating line
Restricted access

We prove that for any collection F of n ≥ 2 pairwise disjoint compact convex sets in the plane there is a pair of sets A and B in F such that any line that separates A from B separates either A or B from a subcollection of F with at least n/18 sets.

  • [1]

    H. Edelsbrunner, A. D. Robison and X. J. Shen. Covering convex sets with non-overlapping polygons. Discrete Mathematics, 81:153-164,1990.

  • [2]

    L. Fejes Tóth. Illumination of convex discs. Acta Mathematica Academiae Scientiarum Hungaricae, 29(3-4):355-360, 1997.

  • [3]

    R. Hope and M. Katchalski. Separating plane convex sets. Mathematica Scandinavica 66(1):44-46, 1990.

  • [4]

    E. Rivera-Campo and J. Törőcsik. On separation of plane convex sets. European Journal of Combinatorics 14:113-116, 1993.

  • [5]

    H. Tverberg. A separation property of plane convex sets. Mathematica Scandinavica 45:255-260, 1979.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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