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Partitioning vertices of a tournament into independent cycles. (English) Zbl 1028.05038
Summary: Let \(k\) be a positive integer. A strong digraph \(G\) is termed \(k\)-connected if the removal of any set of fewer than \(k\) vertices results in a strongly connected digraph. The purpose of this paper is to show that every \(k\)-connected tournament with at least \(8k\) vertices contains \(k\) vertex-disjoint directed cycles spanning the vertex set. This result answers a question posed by Bollobás.

05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
Full Text: DOI
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[4] Song, Z., Complementary cycles of all lengths in tournaments, J. combin. theory ser. B, 57, 18-25, (1993) · Zbl 0723.05062
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