Existence of cyclic k-cycle systems of the complete graph Original Research Article

Starting from earliest papers by Rosa we solve, directly and explicitly, the existence problem for cyclic k-cycle systems of the complete graph Kv with v≡1 (mod 2k), and the existence problem for cyclic k-cycle systems of the complete m-partite graph Km×k with m and k being odd. As a particular consequence, a cyclic p-cycle system of Kv with p being a prime exists for all admissible values of v but (p,v)≠(3,9). This was previously known only for p=3,5,7.