The monochromatic block number Original Research Article

In 1993 Voloshin introduced the concept of mixed hypergraph. A mixed hypergraph is characterised by the fact that it possesses anti-edges as well as edges. In a colouring of a mixed hypergraph, every anti-edge has at least two vertices of the same colour. In this paper a new parameter is introduced: the monochromatic block number mb. It is the number of monochromatic blocks in a colouring of a Steiner system. The exact value of mb is given for every colouring in STS(v). Upper and lower bounds for mb in particular SQSs are found.