Disjoint cycles on Lichiardopol's conjecture in tournaments

Fuhong Ma, Jin Yan

Published 2017-07-08Version 1

In this paper, we give an almost solution to the conjecture by N. Lichiardopol [Discrete Math. 310 (19) (2010) 2567-2570]. It is proved that for given integers $q \geq 11$ and $k \geq 1$, any tournament with minimum out-degree at least $(q-1)k-1$ contains at least $k$ disjoint cycles of length $q$. Our result is also an affirmative answer in terms of tournaments to the conjecture of C. Thomassen [Combinatorca. 3 (3-4) (1983) 393-396]. In addition, it is an extension of a result by J. Bang-Jensen, S. Bessy and S. Thomasse [J.Graph Theory 75 (3) (2014) 284-302].