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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.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
##### Keywords:
strong digraph; strongly connected digraph
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##### References:
 [1] Bondy, J.A.; Murty, U.S.R., Graph theory with applications, (1976), Macmillan London/New York · Zbl 1134.05001 [2] Reid, K.B., Two complementary circuits in two-connected tournaments, (), 321-334 · Zbl 0573.05031 [3] Reid, K.B., Three problems on tournaments, Graph theory and its applications: east and west, Annals of the New York Academy science, 576, (1989), New York Academy of Science New York, p. 466-473 · Zbl 0792.05062 [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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