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Two proofs of Bermond-Thomassen conjecture for regular tournaments

Stéphane Bessy 1 Jean-Sébastien Sereni 2 Nicolas Lichiardopol 3
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
3 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe MC3
Laboratoire I3S - MDSC - Modèles Discrets pour les Systèmes Complexes
Abstract : Bermond-Thomassen conjecture says that a digraph of minimum out-degree at least 2r−1, r >=1, contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r=2, but it is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we present two proofs of this conjecture for regular tournaments. In the first one, we shall prove auxiliary results about union of sets contained in other union of sets, that might be of independent interest. The second one uses a more graph-theoretical approach, by studying the properties of a maximum set of vertex-disjoint directed triangles.
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Contributor : Stephan Thomasse <>
Submitted on : Tuesday, June 12, 2007 - 2:42:38 PM
Last modification on : Monday, October 12, 2020 - 10:30:32 AM



Stéphane Bessy, Jean-Sébastien Sereni, Nicolas Lichiardopol. Two proofs of Bermond-Thomassen conjecture for regular tournaments. 6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Jul 2007, Prague, République Tchèque, Czech Republic. pp.47-53, ⟨10.1016/j.endm.2007.01.008⟩. ⟨lirmm-00153984⟩



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