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We generalize all the results obtained for maximum integer multiflow and minimum multicut problems in trees by Garg, Vazirani and Yannakakis [N. Garg, V.V. Vazirani, M. Yannakakis, Primal-dual approximation algorithms for integral flow and multicut in trees, Algorithmica 18 (1997) 3-20] to graphs with a fixed cyclomatic number, while this cannot be achieved for other classical generalizations of trees. We also introduce the k-edge-outerplanar graphs, a class of planar graphs with arbitrary (butdoi:10.1016/j.dam.2009.03.009 fatcat:sp573pvvnrgdrgb6flpxilanoe