k-Distinct In- and Out-Branchings in Digraphs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

55 Downloads (Pure)


An out-branching and an in-branching of a digraph D are called k-distinct if each of them has k arcs absent in the other. Bang-Jensen, Saurabh and Simonsen (2016) proved that the problem of deciding whether a strongly connected digraph D has k-distinct out-branching and in-branching is fixed-parameter tractable (FPT) when parameterized by k. They asked whether the problem remains FPT when extended to arbitrary digraphs. Bang-Jensen and Yeo (2008) asked whether the same problem is FPT when the out-branching and in-branching have the same root. By linking the two problems with the problem of whether a digraph has an out-branching with at least k leaves (a leaf is a vertex of out-degree zero), we first solve the problem of Bang-Jensen and Yeo (2008). We then develop a new digraph decomposition called the rooted cut decomposition and using it we prove that the problem of Bang-Jensen et al. (2016) is FPT for all digraphs. We believe that the rooted cut decomposition will be useful for obtaining other results on digraphs.
Original languageEnglish
Title of host publication44th International Colloquium on Automata, Languages, and Programming
Subtitle of host publicationICALP 2017
Number of pages13
ISBN (Print)978-3-95977-041-5
Publication statusPublished - 2017

Publication series

NameLeibniz International Proceedings in Informatics
PublisherSchloss Dagstuhl Leibniz Center for Informatics
ISSN (Electronic)1868-8969

Cite this