Abstract

The support of a digraph is the undirected graph arising when directions of edges are ignored. We prove that recognizing supports of line digraphs of digraphs is an NP-Complete problem. Then we observe that solvable cases of the directed max-cut problem arise from solvable cases of the maximum-weight stable set problem via supports of line digraphs; in particular, we investigate digraphs G such that the support of the line digraph of G is perfect.

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