The b-chromatic number of some special families of graphs
01 Nov 2017-Vol. 263, Iss: 4, pp 042113
About: The article was published on 2017-11-01 and is currently open access. It has received None citations till now. The article focuses on the topics: Chromatic scale.
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TL;DR: It is shown that ψ ( G ) can be viewed as the maximum over all minimal elements of a partial order defined on the set of all colourings of G, giving rise to a new parameter, which is called the b-chromatic number, ϑ ( G ), of G.
263 citations
TL;DR: It is shown that the Petersen graph infirms the conjecture that every d-regular graph with girth at least 5 has a b-coloring with d+1 colors, and a new formulation of this question is proposed and given a positive answer for small degree.
46 citations