Disjoint paths in sparse graphs

Cédric Bentz
2009 Discrete Applied Mathematics  
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 (but
more » ... bounded) tree-width that generalizes the cacti, and show that the integrality gap of the maximum edge-disjoint paths problem is bounded in these graphs.
doi:10.1016/j.dam.2009.03.009 fatcat:sp573pvvnrgdrgb6flpxilanoe