Cycle-pancyclism in bipartite tournaments II

Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T , and k an even number. In this paper the following question is studied: What is the maximum intersection with γ of a directed cycle of length k contained in T [V (γ)]? It is proved that for an even k in the range n+6 2 ≤ k ≤ n−2, there exists a directed cycle Ch(k) of length h(k), h(k) ∈ {k, k − 2} with |A(Ch(k)) ∩ A(γ)| ≥ h(k)− 4 and the result is best possible. In a previous paper a similar result for 4 ≤ k ≤ n+4 2 was proved.