Geodesic
On the upper and lower chromatic numbers of BSQSs(16)
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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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($16$).
DOI : 10.37236/1550
Classification : 05C15, 05C65, 51E10
Mots-clés : chromatic number, Steiner quadruple system, mixed hypergraph, vertex colourings 
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     author = {Giovanni Lo Faro and Lorenzo Milazzo and Antoinette Tripodi},
     title = {On the upper and lower chromatic numbers of {BSQSs(16)}},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1550},
     zbl = {0974.05034},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1550/}
}
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Giovanni Lo Faro; Lorenzo Milazzo; Antoinette Tripodi. On the upper and lower chromatic numbers of BSQSs(16). The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1550

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