On the upper and lower chromatic numbers of BSQSs(16)

Abstract

A mixed hypergraph is characterized by the fact that it possesses C-edges as well as D-edges. In a colouring of a mixed hypergraph, every C-edge has at least two vertices of the same colour and every D-edge has at least two vertices coloured di erently. The upper and lower chromatic numbers Χ̄, Χ are the maximum and minimum numbers of colours for which there exists a colouring using all the colours. The concepts of mixed hypergraph, upper and lower chromatic numbers are applied to SQSs. In fact a BSQS is an SQS where all the blocks are at the same time C-edges and D-edges. In this paper we prove that any BSQS(16) is colourable with the upper chromatic number Χ = 3 and we give new information about the chromatic spectrum of BSQSs(16).