Cyclic Hamiltonian cycle systems of the complete graph

Rotational k‐cycle systems of order v < 3k; another proof of the existence of odd cycle systems

“…Recently, the same result with k odd was independently established by Buratti and Del Fra [7], Fu and Wu [9], Bryant, Gavlas, and Ling [3], and by Blinco, El Zanati, and Vanden Eynden [4]. The existence problem for cyclic ðK v ; C k Þ-designs with v k (mod 2k) has been settled by Buratti and Del Fra [8] for k not belonging to the set M ¼ fp e j p prime; e > 1g [ f15g, and Vietri [19] for k 2 M.…”

On the Existence of Elementary Abelian Cycle Systems

“…Many authors have contributed to prove the following Theorem 1.1 which is, so far, the most important result about the existence of cyclic k-cycle systems (see [10], [11], [14], [18], [19], [20], [21], [24]). In what follows we will deal with the existence problem of cycle systems for the elementary abelian case.…”

Strong difference families over arbitrary graphs

“…In spite of this we are still quite far from solving the existence problem for cyclic (K v , C k )-designs. At the moment the answer is known for v congruent to 1 or k (mod 2k) (fruit of the joint efforts of many authors [9,10,22,[25][26][27][28]31]) and for k ≤ 32 or k = 2q with q a prime power [32]. In particular, for q = 3, there exists a cyclic C 6 -decomposition of K v for all admissible values of v with the only definite exception of v = 9.…”