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Vertex-disjoint cycles in regular tournaments. (English) Zbl 1243.05097
Summary: The Bermond – Thomassen conjecture states for \(r\geq 1\), any digraph of minimum out-degree at least \(2r - 1\) contains at least \(r\) vertex-disjoint directed cycles. In a recent paper, Bessy, Sereni and the author proved that a regular tournament \(T\) of degree \(2r - 1\) contains at least \(r\) vertex-disjoint directed cycles, which shows that the above conjecture is true for regular tournaments. In this paper, we improve this result by proving that such a tournament contains at least \(\frac 76 r - \frac 73\) vertex-disjoint directed cycles.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
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[1] Bang-Jensen, J.; Gutin, G., ()
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[3] Bessy, S.; Lichiardopol, N.; Sereni, J.S., Two proofs of the bermond – thomassen conjecture for tournaments with bounded minimum in-degree, Discrete math., 310, 3, 557-560, (2010) · Zbl 1188.05072
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