Edge disjoint paths and max integral multiflow/min multicut theorems in planar graphs
Résumé
We generalize all the results obtained for integer multiflow and
multicut problems in trees by Garg et al. [N. Garg, V.V. Vazirani and M. Yannakakis. Primal-dual approximation algorithms for integral flow and multicut in
trees. Algorithmica 18 (1997), pp. 3-20] to planar
graphs with a fixed number of faces, although other classical
generalizations do not lead to such results. We also introduce the
class of k-edge-outerplanar graphs and bound the
integrality gap for the maximum edge-disjoint paths problem in
these graphs.