Abstract : We consider the following problem for oriented graphs and digraphs: Given an oriented graph (digraph) H, does it contain an induced subdivision of a prescribed digraph D? The complexity of this problem depends on D and on whether H is an oriented graph or contains 2-cycles. We announce a number of examples of polynomial instances as well as several NP-completeness results.
Frédéric Havet, Jørgen Bang-Jensen, Nicolas Trotignon. Finding an induced subdivision of a digraph. VI Latin-American Algorithms, Graphs and Optimization Symposium (LAGOS 2011), Apr 2011, Bariloche, Argentina. pp.09--14. ⟨inria-00638464⟩