  Let $K_4^+$ be the 5-vertex graph obtained from $K_4$, the complete graph on
four vertices, by subdividing one edge precisely once (i.e. by replacing one
edge by a path on three vertices). We prove that if the chromatic number of
some graph $G$ is much larger than its clique number, then $G$ contains a
subdivision of $K_4^+$ as an induced subgraph.
