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Covering the vertices of a digraph by cycles of prescribed length. (English) Zbl 0764.05070
Summary: Let $$D$$ be a strong digraph with $$n$$ vertices and at least $$(n-1)(n-2)+3$$ arcs. For any integers $$k,n_ 1,n_ 2,\dots,n_ k$$ such that $$n=n_ 1+n_ 2+\cdots+n_ k$$ and $$n_ 1\geq 3$$, there exists a covering of the vertices of $$D$$ by disjoint directed cycles of length $$n_ 1,n_ 2,\dots,n_ k$$ except in two cases: Case 1: $$n=6$$; $$n_ 1=n_ 2=3$$ and $$D$$ contains a stable set with 3 vertices. Case 2: $$n=9$$; $$n_ 1=n_ 2=n_ 3=3$$ and $$D$$ contains a stable set with 4 vertices.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles
##### Keywords:
strong digraph; covering; directed cycles; stable set
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##### References:
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