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 ${\displaystyle C_{h\left(k\right)}}$ of length h(k), h(k) ∈ {k,k-2} with ${\displaystyle |A\left(C_{h\left(k\right)}\right)\cap A(\gamma )|\ge h\left(k\right)-4}$ and the result is best possible. In a previous paper a similar result for 4 ≤ k ≤ (n+4)/2 was proved.