Max-multiflow/min-multicut for G+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 ‘‘maxmultiflow = min-multicut for some class’’. © 2011 Elsevier B.V. All rights reserved.