  Fix an oriented graph H, and let G be a graph with bounded clique number and
very large chromatic number. If we somehow orient its edges, must there be an
induced subdigraph isomorphic to H? Kierstead and Rodl raised this question for
two specific kinds of digraph H: the three-edge path, with the first and last
edges both directed towards the interior; and stars (with many edges directed
out and many directed in). Aboulker et al subsequently conjectured that the
answer is affirmative in both cases. We give affirmative answers to both
questions.
