... QuattrocchiDipartimento di Matematica e InformaticaUniversita’ di Catania, Catania, ITALIAquattrocchi@dmi.unict.itSubmitted: January 20, 2001; Accepted: June 5, 2001Abstract A colouring of a 4-cycle system ... {a 0 ,a 1 ,a 2 ,a 3}, Pj= { [a 0 ,a 2 ,a 1], [a 0 ,a 3 ,a 2], [a 0 ,a 1 ,a 3]},F = { (a 0 ,a 2 ,a 1,x), (a 0 ,a 3 ,a 2,y), (a 0 ,a 1 ,a 3,z)}⊆B.Let D(Ωj)={B1,B2, ,Bθ} be the set of 4-cycles ... is the vertex set of Kv and B is an edge-disjoint decomposition of Kvinto copies of the graph G. Usually we say that B is a block of the G-design ifB ∈B,andB is called the block-set. A path...