On the Upper and Lower Chromatic Numbers of BSQSs(16)

Giovanni Lo Faro, Lorenzo Milazzo, Antoinette Tripodi

Abstract


A mixed hypergraph is characterized by the fact that it possesses ${\cal C}$-edges as well as ${\cal D}$-edges. In a colouring of a mixed hypergraph, every ${\cal C}$-edge has at least two vertices of the same colour and every ${\cal D}$-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 ${\cal C}$-edges and ${\cal D}$-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($16$).


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