  A class of graphs G is chi-bounded if the chromatic number of graphs in G is
bounded by a function of the clique number. We show that if a class G is
chi-bounded,then every class of graphs admitting a decomposition along cuts of
small rank to graphs from G is chi-bounded. As a corollary, we obtain that
every class of graphs with bounded rank-width (or equivalently, clique-width)
is chi-bounded.
