...) is maximum if and only if there is a [γ(X ) − κ(X )]. cut-system X such that α(f) = 1 2 For trees with n vertices, an O(n 2 )-time algorithm for computing a maximum integral multiflow f is proposed =-=[2]-=-, while no strongly-polynomial time algorithm is known to general graphs (e.g., see [3]). In a rooted tree, the parent-children relationship among vertices/edges is defined. The parent of a non-root v...

...ut-size γ(X ) is defined to be ∑ {c(Xt) | t ∈ T }. Note that X is not required to be a partition of V . For any pair of a feasible multiflow f and a cut-system of T in (G, T, c), it holds Cherkasskii =-=[1]-=- proved the next result. α(f) ≤ 1 γ(X ). 2 3Theorem 1 A feasible multiflow f in (G, T, c) is maximum if and only if there is a cut-system γ(X ). X such that α(f) = 1 2 Ibaraki et al. [7] proposed an ...