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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
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