Colourings of Voloshin for S2(2,3, v)*
Abstract
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 contains at least two vertices x,y such that f(x)≠f(y). A Steiner System Sλ(t, k, v), with t, k, v, λ∈N, is a pair (S,B) where S is a finite set of v vertices and B is a family of subsets of S, called blocks, such that: 1) each block contains exactly k vertices; 2) for each t-subset T of S, there exist exactly λ blocks containing T. In this paper we study the lower chromatic number and upper chromatic number for systems S2(2,3,v), considered as mixed hypergraphs with C=D.
