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].