Disjoint 3‐Cycles in Tournaments: A Proof of The Bermond–Thomassen Conjecture for Tournaments |
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| Authors: | Jørgen Bang‐Jensen Stéphane Bessy Stéphan Thomassé |
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| Affiliation: | 1. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE, UNIVERSITY OF SOUTHERN DENMARK, ODENSE, DENMARK;2. ALGCO, LIRMM, FRANCE;3. LABORATOIRE LIP (U. LYON, CNRS, ENS LYON, INRIA, UCBL), LYON, FRANCE |
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| Abstract: | We prove that every tournament with minimum out‐degree at least  contains k disjoint 3‐cycles. This provides additional support for the conjecture by Bermond and Thomassen that every digraph D of minimum out‐degree  contains k vertex disjoint cycles. We also prove that for every  , when k is large enough, every tournament with minimum out‐degree at least  contains k disjoint cycles. The linear factor 1.5 is best possible as shown by the regular tournaments. |
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| Keywords: | disjoint cycles tournaments |
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