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Finding complementary cycles in locally semicomplete digraphs. (English) Zbl 1055.05086
Summary: It is well known that the problem of deciding whether a given digraph has a \(k\)-cycle factor for some constant \(k\) (i.e. a collection of \(k\) disjoint cycles that cover all vertices of the digraph) is \(\mathcal{NP}\)-complete as this is a generalization of the Hamilton cycle problem. In this paper, we show that for the class of locally semicomplete digraphs the existence of a 2-cycle factor can be decided, and a 2-cycle factor found if it exists, in time \(\mathcal O(n^3)\), where \(n\) is the order of the digraph.

MSC:
05C38 Paths and cycles
05C20 Directed graphs (digraphs), tournaments
68R10 Graph theory (including graph drawing) in computer science
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