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Journal Articles Journal of Graph Theory Year : 2014

Disjoint 3-Cycles in Tournaments: A Proof of The Bermond-Thomassen Conjecture for Tournaments

Abstract

We prove that every tournament with minimum out-degree at least inline image contains k disjoint 3-cycles. This provides additional support for the conjecture by Bermond and Thomassen that every digraph D of minimum out-degree inline image contains k vertex disjoint cycles. We also prove that for every inline image, when k is large enough, every tournament with minimum out-degree at least inline image contains k disjoint cycles. The linear factor 1.5 is best possible as shown by the regular tournaments.

Dates and versions

lirmm-01282882 , version 1 (04-03-2016)

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Jørgen Bang-Jensen, Stéphane Bessy, Stéphan Thomassé. Disjoint 3-Cycles in Tournaments: A Proof of The Bermond-Thomassen Conjecture for Tournaments. Journal of Graph Theory, 2014, 75 (3), pp.284-302. ⟨10.1002/jgt.21740⟩. ⟨lirmm-01282882⟩
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