The μ-way intersection problem for m-cycle systems Original Research Article

An m-cycle system of order v is a partition of the edge-set of a complete graph of order v into m-cycles. The μ-way intersection problem for m-cycle systems involves taking μ systems, based on the same vertex set, and determining the possible number of cycles which can be common to all μ systems. General results for arbitrary m are obtained, and detailed intersection values for (μ,m)=(3,4),(4,5),(4,6),(4,7),(8,8),(8,9). (For the case (μ,m)=(2,m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (μ,m)=(3,3), see Milici and Quattrocchi (Ars Combin. A 24 (1987) 175).