Complementary cycles in regular bipartite tournaments: a proof of Manoussakis, Song and Zhang Conjecture

Let D be a k-regular bipartite tournament. We show that, for every even p with 4≤p≤|V(D)|−4, D has a cycle C of size p such that D\C is Hamiltonian unless D is isomorphic to a special digraph, F4k. This result proves a conjecture of Manoussakis, Song and Zhang.