Abstract
We prove that the weak k-linkage problem is polynomial for every fixed k for totally i¾?-decomposable digraphs, under appropriate hypothesis on i¾?. 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.
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