On the Arc-Pancyclicity of Local Tournaments

Let \(T = (V,A)\) be a digraph with \(n\) vertices. \(T\) is called a local tournament if for every vertex \(x \in V\), \(T[O(x)]\) and \(T[I(x)]\) are tournaments. In this paper, we prove that every arc-cyclic connected local tournament \(T\) is arc-pancyclic except \(T\cong T_{6}-,T_{8}\)-type digraphs or \(D_8\).