  If a graph has no induced subgraph isomorphic to $H_1$ or $H_2$ then it is
said to be ($H_1,H_2$)-free. Dabrowski and Paulusma found 13 open cases for the
question whether the clique-width of ($H_1,H_2$)-free graphs is bounded. One of
them is the class of ($S_{1,2,2}$,triangle)-free graphs. In this paper we show
that these graphs have bounded clique-width. Thus, also
($P_1+2P_2$,triangle)-free graphs have bounded clique-width which solves
another open problem of Dabrowski and Paulusma. Meanwhile we were informed by
Paulusma that in December 2015, Dabrowski, Dross and Paulusma showed that
($S_{1,2,2}$,triangle)-free graphs (and some other graph classes) have bounded
clique-width.
