k-critically n-connected graphs

A graph G is said to be (n*,k)- connected if it has connectivity n and every set of k vertices is contained in an n-cutset. It is shown that an (n*,k)-connected graph G contains an n-cutset C such that G--C has a component with at most n/(k + 1) vertices. It is conjectured, however, that n/(k + 1) can be replaced with n/2k, and this is shown to be best possible. 2 figures.