  We prove a version of the strong Taylor's conjecture for stable graphs: if
$G$ is a stable graph whose chromatic number is strictly greater than
$\beth_2(\aleph_0)$ then $G$ contains all finite subgraphs of Sh$_n(\omega)$
and thus has elementary extensions of unbounded chromatic number. This
completes the picture from our previous work. The main new model theoretic
ingredient is a generalization of the classical construction of
Ehrenfeucht-Mostowski models to an infinitary setting, giving a new
characterization of stability.
