Before revision: For an unweighted graph on kterminals , Kratsch and Wahlstr\"om constructed a vertex sparsifier  with O(k^3) vertices via the theory of representative families on matroids.
After revision: Let G be a graph and S, T \subseteq V(G) be (possibly overlapping) sets of terminals, |S|=|T|=k. We are interested in computing a vertex sparsifier for terminal cuts in G, i.e., a graph H on a smallest possible number of vertices, where S \cup T \subseteq V(H) and such that for every A \subseteq S and B \subseteq T the size of a minimum (A,B)-vertex cut is the same in G as in H. We assume that our graphs are unweighted and that terminals may be part of the min-cut. In previous work , Kratsch and Wahlstr\"om constructed a vertex sparsifier with O(k^3) vertices via the theory of representative families on matroids.