A family of convex sets in the plane satisfying the $(4,3)$-property can be pierced by nine points

Abstract

We prove that every finite family of convex sets in the plane satisfying the $(4,3)$-property can be pierced by $9$ points. This improves the bound of $13$ proved by Gyárfás, Kleitman, and Tóth in 2001.

The author was supported by NSF grant DMS-1839918 (RTG)