Authors: F. Ma, J. Yan Title: On the number of disjoint 4-cycles in regular tournaments Source: Discussiones Mathematicae Graph Theory Received 30.06.2016, Revised 02.01.2017, Accepted 03.01.2017, doi: 10.7151/dmgt.2020 Abstract: In this paper, we prove that for an integer r ≥ 1, every regular tournament T of degree 3r - 1 contains at least \frac{21}{16}r-\frac{10}{3} disjoint directed 4-cycles. 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. Keywords: regular tournament, C4-free, disjoint cycles Links: PDF