Hamiltonian cycles in -circulant digraphs

Let D be the circulant digraph with n vertices and connection set { 2 , 3 , c } . (Assume D is loopless and has outdegree 3.) Work of S. C. Locke and D. Witte implies that if n is a multiple of 6, c ∈ { ( n / 2 ) + 2 , ( n / 2 ) + 3 } , and c is even, then D does not have a hamiltonian cycle. For all other cases, we construct a hamiltonian cycle in D .