The partition of a strong tournament

A digraph T is strong if for every pair of vertices u and v there exists a directed path from u to v and a directed path from v to u. Denote the in-degree and out-degree of a vertex v of T by d-(v) and d+(v), respectively. We define δ-(T)=minv∈V(T){d-(v)} and δ+(T)=minv∈V(T){d+(v)}. Let T0 be a 7-tournament which contains no transitive 4-subtournament. In this paper, we obtain some conditions on a strong tournament which cannot be partitioned into two cycles. We show that a strong tournament T with n⩾6 vertices such that T≇T0 and max{δ+(T),δ-(T)}⩾3 can be partitioned into two cycles. Finally, we give a sufficient condition for a tournament to be partitioned into k cycles.