| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 434820 | Theoretical Computer Science | 2012 | 7 Pages |
We prove that a number of natural problems concerning the existence of arc-disjoint directed and “undirected” (spanning) subdigraphs in a digraph are NP-complete. Among these are the following of which the first settles an open problem due to Thomassé (see e.g. Bang-Jensen and Gutin (2009) [1, Problem 9.9.7], and Bang-Jensen and Kriesell (2009) [5,4]) and the second settles an open problem posed in Bang-Jensen and Kriesell (2009) [5]. •Given a directed graph D and a vertex s of D; does D contain an out-branching rooted at s such that the digraph remains connected (in the underlying sense) after removing all arcs of ?•Given a strongly connected directed graph D; does D contain a spanning strong subdigraph D′ such that the digraph remains connected (in the underlying sense) after removing all arcs of D′?
