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    k-distinct in- and out-branchings in digraphs

    Gutin, G.Z. and Reidl, Felix and Wahlström, M. (2018) k-distinct in- and out-branchings in digraphs. Journal of Computer and System Sciences 95 , pp. 86-97. ISSN 0022-0000.

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    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 and using it prove that the problem of Bang-Jensen et al. (2016) is FPT for all digraphs.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Felix Reidl
    Date Deposited: 27 Feb 2019 12:54
    Last Modified: 09 Aug 2023 12:45


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