Abstract
An out-tree T is an oriented tree with exactly one vertex of in-degree zero and a vertex x of T is called internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a subgraph isomorphic to a given out-tree with k vertices. Both algorithms run in O *(5.704k) time. We apply the deterministic algorithm to obtain an algorithm of runtime O *(c k), where c is a constant, for deciding whether an input digraph contains a spanning out-tree with at least k internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM’08).
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Cohen, N., Fomin, F.V., Gutin, G., Kim, E.J., Saurabh, S., Yeo, A. (2009). Algorithm for Finding k-Vertex Out-trees and Its Application to k-Internal Out-branching Problem. In: Ngo, H.Q. (eds) Computing and Combinatorics. COCOON 2009. Lecture Notes in Computer Science, vol 5609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02882-3_5
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DOI: https://doi.org/10.1007/978-3-642-02882-3_5
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