Arc-disjoint spanning sub(di)graphs in digraphs

Authors:
Jørgen Bang-Jensen;Anders Yeo
Affiliations:
Department of Mathematics and Computer Science, University of Southern Denmark, Odense DK-5230, Denmark;Department of Computer Science, Royal Holloway, University of London, Egham Surrey TW20 0EX, United Kingdom
Venue:
Theoretical Computer Science
Year:
2012

Citing 5
Cited 2

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Combinatorica
Digraphs: Theory, Algorithms and Applications

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Disjoint directed and undirected paths and cycles in digraphs

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On the problem of finding disjoint cycles and dicycles in a digraph

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Decomposing locally semicomplete digraphs into strong spanning subdigraphs

Journal of Combinatorial Theory Series B

Partitioning the arcs of a digraph into a star forest of the underlying graph with prescribed orientation properties

Theoretical Computer Science
Note: Arc-disjoint paths and trees in 2-regular digraphs

Discrete Applied Mathematics

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Abstract

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 Thomasse (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 B"s^+ rooted at s such that the digraph remains connected (in the underlying sense) after removing all arcs of B"s^+? *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^'?