Convex Sets in the Plane with Three of Every Four Meeting

Combinatorica volume 21, pages221–232(2001)Cite this article

Dedicated to the memory of Paul Erdős

Suppose we have a finite collection of closed convex sets in the plane, (which without loss of generality we can take to be polygons). Suppose further that among any four of them, some three have non-empty intersection. We show that 13 points are sufficient to meet every one of the convex sets.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

US$ 39.95

Tax calculation will be finalised during checkout.

Author information

Affiliations

  1. Massachusetts Institute of Technology; 77 Massachusetts Avenue, Cambridge MA 02139, USA; E-mail: djk@math.mit.edu, US

    Daniel J. Kleitman

  2. Computer and Automation Research Institute, Hungarian Academy of Sciences; 1111 Budapest, Kende u. 13–17, Hungary; E-mail: gyarfas@luna.aszi.sztaki.hu, HU

    András Gyárfás

  3. Massachusetts Institute of Technology; 77 Massachusetts Avenue, Cambridge MA 02139, USA; and Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences; 1053 Budapest, Reáltanoda u. 13-15., Hungary; E-mail: toth@math.mit.edu, HU

    Géza Tóth

Authors
  1. Daniel J. Kleitman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. András Gyárfás
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Géza Tóth
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received October 27, 1999/Revised April 11, 2000

RID="*"

ID="*" Supported by grant OTKA-T-029074.

RID="†"

ID="†" Supported by NSF grant DMS-99-70071, OTKA-T-020914 and OTKA-F-22234.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Kleitman, D., Gyárfás, A. & Tóth, G. Convex Sets in the Plane with Three of Every Four Meeting. Combinatorica 21, 221–232 (2001). https://doi.org/10.1007/s004930100020

Download citation

  • AMS Subject Classification (2000) Classes:  52A35