On the Number of Vertex-Disjoint Cycles in Digraphs

@article{Bai2019OnTN,
title={On the Number of Vertex-Disjoint Cycles in Digraphs},
author={Y. Bai and Y. Manoussakis},
journal={SIAM J. Discret. Math.},
year={2019},
volume={33},
pages={2444-2451}
}

Let $k$ be a positive integer. Bermond and Thomassen conjectured in 1981 that every digraph with minimum outdegree at least $2k-1$ contains $k$ vertex-disjoint cycles. It is famous as one of the one hundred unsolved problems selected in [Bondy, Murty, Graph Theory, Springer-Verlag London, 2008]. Lichiardopol, Por and Sereni proved in [SIAM J. Discrete Math. 23 (2) (2009) 979-992] that the above conjecture holds for $k=3$.
Let $g$ be the girth, i.e., the length of the shortest cycle, of a given… Expand