2-Regular equicolourings for -designs

Let G be a graph. Then a G -decomposition of K v , a complete graph on v vertices, is a pair Σ = ( X , B ) , where X is the vertex set of K v and B is a partition of the edge set of K v into graphs all isomorphic to G . The elements of B are called blocks and Σ is said to be a G -design of order v . s paper we study colourings of P 4 -designs where, in each block of B , two vertices are assigned the same colour and the other two another colour. We determine, among other things, families of P 4 -designs having a chromatic spectrum with gaps. These are the only known cases of G -designs having this property except for the families of P 3 -designs found by Lucia Gionfriddo.