Recognizing digraphs of Kelly-width 2 Original Research Article

Kelly-width is a parameter of digraphs recently proposed by Hunter and Kreutzer as a directed analogue of treewidth. We give an alternative characterization of digraphs of bounded Kelly-width in support of this analogy, and the first polynomial-time algorithm recognizing digraphs of Kelly-width 2. For an input digraph image the algorithm outputs a vertex ordering and a digraph image with image witnessing either that image has Kelly-width at most 2 or that image has Kelly-width at least 3, in time linear in image.