Part of this work was done while the first author was on sabbatical at AlGCo, LIRMM, Université Montpellier 2, France whose hospitality is gratefully acknowledged. Financial support from the Danish National Science research council (FNU) (under grant no. 09-066741) is gratefully acknowledged.Contract grant sponsor: ANR GRATOS; Contract grant number: ANR-09-JCJC-0041-01 (to S.B.).
Disjoint 3-Cycles in Tournaments: A Proof of The Bermond–Thomassen Conjecture for Tournaments†
Article first published online: 12 MAR 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 3, pages 284–302, March 2014
How to Cite
Bang-Jensen, J., Bessy, S. and Thomassé, S. (2014), Disjoint 3-Cycles in Tournaments: A Proof of The Bermond–Thomassen Conjecture for Tournaments. J. Graph Theory, 75: 284–302. doi: 10.1002/jgt.21740
- Issue published online: 6 JAN 2014
- Article first published online: 12 MAR 2013
- Manuscript Accepted: 15 FEB 2013
- Manuscript Revised: 7 FEB 2013
- Manuscript Received: 22 JUL 2011
- Danish National Science research council. Grant Number: 09-066741
- ANR GRATOS. Grant Number: ANR-09-JCJC-0041-01
- disjoint cycles;
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.