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 ofB are called blocks andΣ is said to be a G-design of order v. In this paper we study colourings of P4-designs where, in each block of B, two vertices are assigned the same colour and the other two another colour.Wedetermine, among other things, families of P4-designs having a chromatic spectrum with gaps. These are the only known cases of G-designs having this property except for the families of P3-designs found by Lucia Gionfriddo.
2-Regular equicolourings for P4-designs
Gionfriddo M;MILAZZO, Lorenzo Maria Filippo
2012-01-01
Abstract
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 ofB are called blocks andΣ is said to be a G-design of order v. In this paper we study colourings of P4-designs where, in each block of B, two vertices are assigned the same colour and the other two another colour.Wedetermine, among other things, families of P4-designs having a chromatic spectrum with gaps. These are the only known cases of G-designs having this property except for the families of P3-designs found by Lucia Gionfriddo.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
