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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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##### References:
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