Before revision:  In particular, we{\sc  {\sc   show that the problem is strongly NP-complete in the classes of bipartite graphs and their line graphs, and solvable in pseudo-polynomial time in the classes of cocomparability graphs and biconvex bipartite graphs  .
After revision:  In particular, we{\sc {\sc show that the problem is strongly NP-hard for bipartite graphs and their line graphs, and solvable in pseudo-polynomial time in the classes of cocomparability graphs and biconvex bipartite graphs .