Arc-Disjoint Paths in Decomposable Digraphs
We prove that the weak k-linkage problem is polynomial for every fixed k for totally ?-decomposable digraphs, under appropriate hypothesis on ?. We then apply this and recent results by Fradkin and Seymour (on the weak k-linkage problem for digraphs of bounded independence number or bounded cut-width) to get polynomial algorithms for some classes of digraphs like quasi-transitive digraphs, extended semicomplete digraphs, locally semicomplete digraphs (all of which contain the class of semicomplete digraphs as a subclass) and directed cographs.
arc-disjoint paths decomposable digraph quasi-transitive digraph locally semicomplete digraph weak linkages modular partition cut-width