A family of convex sets in the plane satisfying the (4, 3)-property can be pierced by nine points (Q2172657)

The author proves that if \(C\) is a finite family of convex sets in \(\mathbb{R}^2\) such that for any four sets, three have a point in commom, then there is a set of size at most 9 points intersecting every element in \(C\). The result improves the bound of 13 points presented in [\textit{D. J. Kleitman} et al., Combinatorica 21, No. 2, 221--232 (2001; Zbl 0981.52001)] for this problem. The paper contains 26 figures that help the reader.