Finding an induced subdivision of a digraph.

Abstract : We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) G, does it contain an induced subdivision of a prescribed digraph D? The complexity of this problem depends on D and on whether G must be an oriented graph or is allowed to contain 2-cycles. We give a number of examples of polynomial instances as well as several NP-completeness proofs.
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Jørgen Bang-Jensen, Frédéric Havet, Nicolas Trotignon. Finding an induced subdivision of a digraph.. Theoretical Computer Science, Elsevier, 2012, 443, pp.10--24. ⟨hal-00749187⟩

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