Skolem-type difference sets for cycle systems (Q1422122)

Summary: Cyclic \(m\)-cycle systems of order \(v\) are constructed for all \(m \geq 3\), and all \(v\equiv 1\pmod {2m}\). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic \(m\)-cycle system of \(K_v - F\) for all \(m\geq 3\), and all \(v\equiv 2\pmod {2m}\).