Given a finite set V and a set function f : 2(V) bar right arrow Z, we consider the problem of constructing an undirected multigraph G = (V,E) such that the cut function C-G: 2(V) bar right arrow Z of G and f together has value at least 2 for all non-empty and proper subsets of V. If f is intersecting submodular and posi-modular, and satisfies the tripartite inequality, then we show that such a multigraph G with the minimum number of edges can be found in O((T-f + 1)n(4) log n) time, where n = |V| and T is the time to compute the value of f(X) for a subset X subset of V.