Skolem-type Difference Sets for Cycle Systems

Abstract

Cyclic $m$-cycle systems of order $v$ are constructed for all $m\geq 3$, and all $v\equiv 1(\hbox{mod }2m)$. 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 $v\equiv 2(\hbox{mod }2m)$.