Alberto Amato

• University of Catania

Let G be a graph. Then a G-decomposition of Kv, a complete graph on v vertices, is a pair Σ=(X,B), where X is the vertex set of Kv and B is a partition of the edge set of Kv 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. In this paper we study colourings of P 4-designs where, in each...

Let G=(V,E) be a multigraph, without loops. For every vertex x, let E x be the set of the edges of G that are incident to x. An edge colouring f of G is said to be an h-equipartite edge colouring of G, for a fixed h∈N, h≥2, if for every x∈V such that |E x |=hq x +r x , 0≤r x <h, there exists a partition of E x in q x colour classes of cardinality h...

A mixed hypergraph is a triple H=(S,C,D), where S is the vertex set and each of C,D is a family of not-empty subsets of S, the C-edges and D-edges respectively. A strict k-colouring of H is a surjection f from the vertex set into a set of colours {1,2,... ,k} so that each C-edge contains at least two vertices x,y such that f(x)=f(y) and each D-edge...

A mixed hypergraph is a triple H=(S,C,D), where S is the vertex set and each of C,D is a family of not-empty subsets of S, the C-edges and D-edges respectively. A strict kappa-colouring of H is a surjection f from the vertex set into a set of colours { 1,2, center dot center dot center dot kappa) so that each C-edge contains at least two vertices x...

We consider a strict k-colouring of a multigraph G as a sur- jection f from the vertex set of G into a set of colours f1,2,...,kg such that, for every non-pendant vertex x of G, there exist at least two edges incident to x and coloured by the same colour. The maximum number of colours in a strict edge colouring of G is called the upper chromatic in...

A P 3 -design of order v, briefly a P 3 (v), is an uniform hypergraph H=(S,B) with dimension 2 such that: (1) each edge {x,y,z}∈B is supposed to contain the pairs {x,y}, {y,z} but not {x,z}; (2) each pair of items of S belongs to exactly one edge of B. It is possible to prove that a P 3 (v) exists if and only if v≡0 or v≡1(mod4). Given a set S with...

A mixed hypergraph is a triple H=(S,C,D), where S is the vertex set and each of C,D is a family of not-empty subsets of S, the C-edges and D-edges respectively. A strict k-colouring of H is a surjection f from the vertex set into a set of colours {1, 2, . . . , k} so that each C-edge contains at least two distinct vertices x, y such that f(x) = f(y...