  We examine indivisibility for classes of graphs. We show that the class of
hereditarily $\alpha$-sparse graphs is indivisible if and only if $\alpha > 2$.
Additionally, we show that the following classes of graphs are indivisible:
perfect graphs, cographs, and chordal graphs, and the following classes of
graphs are not indivisible: threshold graphs, split graphs, and
distance-hereditary graphs.
