A family of convex sets in the plane satisfying the $(4,3)$-property can be pierced by nine points
Daniel McGinnis · arXiv (Cornell University) · 2020
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.