On the number of disjoint 4-cycles in regular tournaments
Fuhong Ma, Yan Jin · Discussiones Mathematicae Graph Theory · 2017
In this paper, we prove that for an integer r ≥ 1, every regular tournament T of degree 3r -1 contains at least 21 16 r -10 3 disjoint directed 4cycles.Our result is an improvement of Lichiardopol's theorem when taking q = 4 [Discrete Math.310 (2010) 2567-2570]: for given integers q ≥ 3 and r ≥ 1, a tournament T with minimum out-degree and in-degree both at least (q -1)r -1 contains at least r disjoint directed cycles of length q.