Large sets of cycle systems on nine points

Bryant, D. E.; Grannell, Mike and Griggs, Terry (2005). Large sets of cycle systems on nine points. Journal of Combinatorial Mathematics and Combinatorial Computing, 53, pp. 95–102.

Abstract

An $m$ -cycle system of order $v$ , denoted by $m$ CS( $v$ ), is a decomposition of the complete graph $K_v$ into $m$ -cycles. We discuss two types of large sets of $m$ CS( $v$ ) and construct examples of both types for $(m,v)=(4,9)$ and one type for $(m,v)=(6,9)$ . These are the first large sets of cycle systems constructed with $m>3$ , apart from the Hamiltonian cycle decompositions given by Bryant in 1998.