2017/06/02 by Wang, Maoqun, Yang, Weihua
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.00691
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. Bessy, Sereni and Lichiardopol proved that a regular tournament T of minimum degree 2r-1 contains at least r vertex-disjoint directed cycles, which shows that the above conjecture is true for tournaments. After that, Lichiardopol improved this result by showing that a 2r-1-regular tournament contains at least (7)/(6)r-(7)/(3) vertex-disjoint directed cycles. In this paper, we will extend the result to tournaments with minimum out-degree at least 2r-1 by proving a more general result.