A counterexample to conjecture 18.5 in "Geometric Etudes in Combinatorial Mathematics", second edition

A collection of sets $\text{Fscr}$ has the $(p,q)$-property if out of every $p$ elements of $\text{Fscr}$ there are $q$ that have a point in common. A transversal of a collection of sets $\text{Fscr}$ is a set $A$ that intersects every member of $\text{Fscr}$. Gr"unbaum conjectured that every family $\text{Fscr}$ of closed, convex sets in the plane with the $(4,3)$-property and at least two elements that are compact has a transversal of bounded cardinality. Here we construct a counterexample to his conjecture. On the positive side, we also show that if such a collection $\text{Fscr}$ contains two {\em disjoint} compacta then there is a transveral of cardinality at most 13.