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Convex Sets in the Plane with Three of Every Four Meeting

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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.

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Authors and 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
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  2. András Gyárfás
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  3. Géza Tóth
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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.

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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

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