Cycles of all lengths in arc-3-cyclic semicomplete digraphs

AbstractLet D be an arc-3-cyclic, semicomplete digraph and uv be an arc of D contained in a cycle of length r. If vu ∉ A(D) then the arc uv is contained in cycles of length h : 3 ⩽ h ⩽ r, or if δ+(D), δ−(D) ⩾ 3 then the arc uv is contained in cycles of length h : 6 ⩽ h ⩽ r. Also included in this paper is a very useful crossing arc theorem