On decomposing Kn−I into cycles of a fixed odd length Original Research Article

We show that if Kn−I, the complete graph on n vertices with a 1-factor removed, can be decomposed into cycles of a fixed odd length m for all n in the range m⩽n<3m that satisfy the obvious necessary conditions, then Kn−I can be decomposed into m-cycles for all n⩾m satisfying the necessary conditions.