12. (CLZ, Chapter 4, Q25]) Let G be a k-edge-connected graph and let S and T be nonempty disjoint subsets of V(G). Prove that there exist k edge-disjoint paths P1, P2, ..., Pk in G such that each of them is a (u, v)-path for some u ES and v ET (but the pairs (u, v) may be different for different paths) and V(P) n = V(P) T = 1. 12. (CLZ, Chapter 4, Q25]) Let G be a k-edge-connected graph and let S and T be nonempty disjoint subsets of V(G). Prove that there exist k edge-disjoint paths P1, P2, ..., Pk in G such that each of them is a (u, v)-path for some u ES and v ET (but the pairs (u, v) may be different for different paths) and V(P) n = V(P) T = 1