A mixed version of Menger's theorem (Q1180411)

Let be \(G\) a multi(di)graph without loops. Here the authors proved the following common generalization of Menger's theorem for vertex and edge connectivity: There exists \(\lambda\) edge-disjoint unions of \(n\) internally disjoint \(a,b\)-paths iff for any \(k\), \(0\leq k\leq\min\{n- 1,| V(G)|-2\}\) and for any subset \(X\) of \(V(G)-\{a,b\}\) with cardinality \(k\), \(G-X\) is \(\lambda(n-k)\)-edge-connected between \(a\) and \(b\).