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An arc in a tournament T with n ≥ 3 vertices is called k-pancyclic, if it belongs to a cycle of length l for all k ≤ l ≤ n. In this paper, the result that each s-strong (s ≥ 3) tournament T contains at least s + 2 out-arc 5-pancyclic vertices is obtained. Furthermore, our proof yields a polynomial algorithm to find s + 2 out-arc 5-pancyclic vertices of T .
An arc in a tournament T with n ≥ 3 vertices is called pancyclic if it belongs to a cycle of length l for all 3 ≤ l ≤ n. We call a vertex u of T an out-arc pancyclic vertex of T if each out-arc of u is pancyclic in T . Yao, Guo and Zhang [Discrete Appl. Math. 99 (2000), 245–249] proved that every strong tournament contains at least one out-arc pancyclic… (More)