Two proofs of the Bermond-Thomassen conjecture for tournaments with bounded minimum in-degree

The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r -1 contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r = 2, and very recently the conjecture was proved for the case where r = 3. It is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we present two proofs of this

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Stéphane Bessy, Nicolas Lichiardopol, Jean-Sébastien Sereni
• Keywords: Bermond-Thomassen Conjecture, DM 2010, Minimum Out-degree, Positive Integer