Characterization and Recognition of Digraphs of Bounded Kelly-width
Kelly-width is a parameter of directed graphs recently proposed by Hunter and Kreutzer as a directed analogue of treewidth. We give several alternative characterizations of directed graphs of bounded Kelly-width in support of this analogy. We apply these results to give the first polynomial-time algorithm recognizing directed graphs of Kelly-width 2. For an input directed graph G = (V, A) the algorithm will output a vertex ordering and a directed graph H = (V, B) with A ⊆ B witnessing either that G has Kelly-width at most 2 or that G has Kelly-width at least 3, in time linear in H.
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