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: For an unweighted graph on kterminals , Kratsch and Wahlstr\"om (FOCS 2012/JACM 2020) used connections to matroid theory to show that a vertex sparsifier with O(k^3) vertices via the theory of representative families on matroids.