Convex Sets in the Plane with Three of Every Four Meeting

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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Received October 27, 1999/Revised April 11, 2000

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

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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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  • AMS Subject Classification (2000) Classes:  52A35