Complementary Cycles of All Lengths in Tournaments

In this paper, the following theorem and some related problems are investigated.THEOREM. Let T be a 2-connected n-tournament with n ≥ 6. Then T contains two vertex-disjoint cycles of lengths k and n − k for any integer k with n − 3 ≥ k ≥ 3, unless T is isomorphic to the 7-tournament which contains no transitive 4-tournament.