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 differently. The upper and lower chromatic numbers \bar(\chi), \chi 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 \bar(\chi) = 3 and we give new information about the chromatic spectrum of BSQSs(16).

### On the upper and lower chromatic numbers of BSQS(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 differently. The upper and lower chromatic numbers \bar(\chi), \chi 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 \bar(\chi) = 3 and we give new information about the chromatic spectrum of BSQSs(16).
##### Scheda breve Scheda completa Scheda completa (DC)
2001
Steiner system; Colouring, ; Chromatic number
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/21303
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