On decomposition of r-partite graphs into edge-disjoint hamilton circuits

Let K(n;r) denote the complete r-partite graph K(n, n,…, n). It is shown here that for all even n(r ? 1) ? 2, K(n;r) is the union of $\text{n(r ? 1)}\text{2}$ of its Hamilton circuits which are mutually edge-disjoint, and for all odd n(r ? 1) ? 1, K(n;r) is the union of $\text{(n(r ? 1) ? 1)}\text{2}$ of its Hamilton circuits and a 1-factor, all of which are mutually edge-disjoint.