A forcing dichotomy for weak Borel chromatic numbers of closed graphs.

**Abstract.** We show that for a closed graph on an analytic Hausdorff space
the following dichotomy holds: Either the graph has large cliques
or the weak Borel chromatic number can be forced to be small.
The weak Borel chromatic number of a graph G is the least size of a partition of the
space of vertices into Borel sets that contain at most one vertex of every edge.
This is joint work with Clinton Conley and Ben Miller.