A mixed hypergraph is characterized by the fact that it possesses CC-edges as well as DD-edges. In a colouring of a mixed hypergraph, every CC-edge has at least two vertices of the same colour and every DD-edge has at least two vertices coloured differently. The upper and lower chromatic numbers χ¯χ¯, χχ 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 SQSsSQSs. In fact a BSQS is an SQS where all the blocks are at the same time CC-edges and DD-edges. In this paper we prove that any BSQS(16)BSQS(16) is colourable with the upper chromatic number χ¯=3χ¯=3 and we give new information about the chromatic spectrum of BSQSs(1616).
On the upper and lower chromatic numbers of BSQS(16)
LO FARO, Giovanni;TRIPODI, Antoinette
2001-01-01
Abstract
A mixed hypergraph is characterized by the fact that it possesses CC-edges as well as DD-edges. In a colouring of a mixed hypergraph, every CC-edge has at least two vertices of the same colour and every DD-edge has at least two vertices coloured differently. The upper and lower chromatic numbers χ¯χ¯, χχ 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 SQSsSQSs. In fact a BSQS is an SQS where all the blocks are at the same time CC-edges and DD-edges. In this paper we prove that any BSQS(16)BSQS(16) is colourable with the upper chromatic number χ¯=3χ¯=3 and we give new information about the chromatic spectrum of BSQSs(1616).Pubblicazioni consigliate
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