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Complementary pairs of graphs orientable to line digraphs. (English) Zbl 0781.05044
Summary: A graph is orientable to a line digraph (OLD, for short) if its lines can be oriented in such a way that the resulting digraph is the line digraph of some digraph. We find all graphs such that both the graph and its complement are OLD and also characterize these graphs in terms of minimal forbidden subgraphs. As shown, all of these graphs have at most nine points.
MSC:
05C75 Structural characterization of families of graphs
05C20 Directed graphs (digraphs), tournaments
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