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.


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.

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