On Alspachʹs conjecture with two even cycle lengths Original Research Article

For m,n even and n>m, the obvious necessary conditions for the existence of a decomposition of the complete graph Kv when v is odd (or the complete graph with a 1-factor removed Kv⧹F when v is even) into r m-cycles and s n-cycles are shown to be sufficient if and only if they are sufficient for v<7n. This result is used to settle all remaining cases with m,n⩽10.