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. Since their breakthrough result in 2012, no improvement upon the O(k^3) bound has been found .
After revision: For an unweighted graph on kterminals , Kratsch and Wahlstr\"om constructed a vertex sparsifier with O(k^3) vertices can be computed in randomized polynomial time, even for arbitrary digraphs G. However, since then, no improvements on the size O(k^3) bound has been found .