Max-multiflow/min-multicut for G plus H series-parallel

We give a new characterization of series-parallel graphs which implies that the maximum integer multiflow is equal to the minimum capacity multicut if G + H is series-parallel, where G + H denotes the union of the support graph G and the demand graph H. We investigate the difference between a result of the type the cut-condition is sufficient for the existence of a multiflow in some class" and a result of the type "max-multiflow = min-multicut for some class". (C) 2011 Elsevier B.V. All rights reserved.