  What is the minimum number of colors that always suffice to color every
planar set of points such that any disk that contains enough points contains
two points of different colors? It is known that the answer to this question is
either three or four. We show that three colors always suffice if the condition
must be satisfied only by disks that contain a fixed point. Our result also
holds, and is even tight, when instead of disks we consider their topological
generalization, namely pseudo-disks, with a non-empty intersection. Our
solution uses the equivalence that a hypergraph can be realized by stabbed
pseudo-disks if and only if it is ABAB-free. These hypergraphs are defined in a
purely abstract, combinatorial way and our proof that they are 3-chromatic is
also combinatorial.
