Geodesic
A conjecture on cycle-pancyclism in tournaments
Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 243-251

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Let T be a hamiltonian tournament with n vertices and γ a hamiltonian cycle of T. In previous works we introduced and studied the concept of cycle-pancyclism to capture the following question: What is the maximum intersection with γ of a cycle of length k? More precisely, for a cycle Cₖ of length k in T we denote I_γ (Cₖ) = |A(γ)∩A(Cₖ)|, the number of arcs that γ and Cₖ have in common. Let f(k,T,γ) = maxI_γ(Cₖ)|Cₖ ⊂ T and f(n,k) = minf(k,T,γ)|T is a hamiltonian tournament with n vertices, and γ a hamiltonian cycle of T. In previous papers we gave a characterization of f(n,k). In particular, the characterization implies that f(n,k) ≥ k-4.
Keywords: Tournaments, pancyclism, cycle-pancyclism 
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Galeana-Sánchez, Hortensia; Rajsbaum, Sergio. A conjecture on cycle-pancyclism in tournaments. Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 243-251. http://geodesic.mathdoc.fr/item/DMGT_1998_18_2_a10/