Large Sets of Cycle Systems on Nine Points

Abstract

An $m$-cycle system of order $v$, denoted by $mCS(v)$, is a decomposition of the complete graph $K_v$ into $m$-cycles. We discuss two types of large sets of $mCS(v)$ 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 in [2].