Bondy, J. A.; Hell, Pavol A note on the star chromatic number. (English) Zbl 0706.05022 J. Graph Theory 14, No. 4, 479-482 (1990). Let k and d be positive integers such that \(k\geq 2d\). A (k,d)-colouring of a graph G is a mapping c from the set of vertices of G to \({\mathbb{Z}}_ k\) such that \(\min \{| c(u)-c(v)|,\quad k-| c(u)-c(v)| \}\geq d\) for each edge \(\{\) u,v\(\}\). The star chromatic number \(\chi^*(G)\) of a graph G is defined by \(\chi^*(G):=\inf \{k/d:\;G\quad has\quad a\quad (k,d)-colouring\}.\) A. Vince [J. Graph Theory 12, 551-559 (1988; Zbl 0658.05028)] introduced (k,d)-colourings and the star chromatic number of a graph as a generalization of graph colouring. The present note yields shorter proofs and offers further insight. Reviewer: U.Baumann Cited in 1 ReviewCited in 72 Documents MSC: 05C15 Coloring of graphs and hypergraphs Keywords:(k,d)-colouring; star chromatic number Citations:Zbl 0658.05028 PDFBibTeX XMLCite \textit{J. A. Bondy} and \textit{P. Hell}, J. Graph Theory 14, No. 4, 479--482 (1990; Zbl 0706.05022) Full Text: DOI References: [1] Albertson, Discrete Math. 54 pp 127– (1985) [2] Hell, J. Combinat. Theory Ser. B 48 pp 92– (1990) [3] Vince, J. Graph Theory 12 pp 551– (1988) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.