5-cycle systems of \(\lambda(K_v-K_u)\) (Q2747190)

The multigraph \(\lambda (K_v - K_u)\) is a graph on a vertex set \(V\), \(|V|= v\), with a set \(U\subseteq V\), \(|U|= u\), in which there are exactly \(\lambda\) edges between each pair of vertices \(a,b\in V\), where \(a\) or \(b\) is not in \(U\). The author characterizes all positive integers \(\lambda, v\), and \(u\) such that the edges of \(\lambda (K_v - K_u)\) can be partitioned into 5-element subsets each of which forms a 5-cycle in \(\lambda (K_v - K_u)\).