Decomposing the complete graph into cycles of many lengths (Q1895814)

The authors show the existence of a solution to Alspach's problem when the cycle lengths are ``as distinct as possible'': for \(v\) odd, the complete graph on \(v\) vertices can be decomposed into \(v-2\) cycles of lengths \(3, 3, 4, 5, \dots, v - 1\) if \(v \geq 3\), and into \(v - 3\) cycles of lengths \(3, 4, \dots, v - 4, v - 2, v - 1,v\) if \(v \geq 7\).