We study the VC-dimension of the set system on the vertex set of some graph
which is induced by the family of its k-connected subgraphs. In particular,
we give tight upper and lower bounds for the VC-dimension. Moreover, we show
that computing the VC-dimension is NP-complete and that it remains
NP-complete for split graphs and for some subclasses of planar
bipartite graphs in the cases k=1 and k=2. On the positive side, we
observe it can be decided in linear time for graphs of bounded clique-width