Finding an induced subdivision of a digraph

Authors:
Jørgen Bang-Jensen;Frédéric Havet;Nicolas Trotignon
Affiliations:
Department of Mathematics and Computer Science, University of Southern Denmark, Odense DK-5230, Denmark;Projet Mascotte, I3S (CNRS, UNSA) and INRIA, Sophia Antipolis, France;CNRS, LIPENS Lyon, France
Venue:
Theoretical Computer Science
Year:
2012

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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.