On diagonal cycle systems

A diagonal cycle is a cycle of length 2n together with one edge between two vertices at distance n in the cycle. For example, /{4 e is a cycle of length fonr with one extra edge between two vertices at distance two in the cycle. Methods for decomposing the complete graph Kv into diagonal cycles are given when v == 0 (mod 2n + 1) if n is odel, and when v == 1 (mod 2n + 1), if n 3 (mod 4); in the case n 1 (mod 4) further partial results are obtained.