Cycle-pancyclism in tournaments III

Let T be a hamiltonian tournament with n vertices and a hamiltonian cycle of T. For a cycle C k of length k in T we denote I (C k) = jA() \ A(C k)j, the number of arcs that and C k have in common. Let f(n; k; T;) = maxfI (C k)jC k Tg and f(n; k) = minff(n; k; T;)jT is a hamiltonian tournament with n vertices, and a hamiltonian cycle of Tg. In a previous paper 3] we studied the case of n 2k ? 4 and proved that f(n; 3) = 1, f(n; 4) = 1 and f(n; 5) = 2 if n 6 = 2k ? 2; f(n; k) = k ? 1 if and only if n = 2k ? 2; for k > 5, f(n; k) = k ? 2 if and only if n 2k ? 4, n 6 = 2k ? 2 and n k (mod k ? 2); for k > 5, f(n; k) = k ? 3 if and only if n 2k ? 4 and n 6 6 k (mod k ? 2). In this paper we consider the case of n 2k ? 5 and complete the description of f(n; k) by proving that f(n; k) = k ? 4 if and only if n 2k ? 5.