The achromatic number of a graph
TLDR
The chromatic number χ(G) is the minimum number of colors required for (a complete coloring of) the points of a graph G, while the achromatic number is the maximum such number as discussed by the authors.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1970-03-01 and is currently open access. It has received 104 citations till now. The article focuses on the topics: Complete coloring & Graph power.read more
Citations
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Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
Journal ArticleDOI
The b-chromatic number of a graph
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.
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A survey of Nordhaus-Gaddum type relations
Mustapha Aouchiche,Pierre Hansen +1 more
TL;DR: In this paper, Nordhaus and Gaddum gave lower and upper bounds on the sum and product of the chromatic number of a graph and its complement, in terms of the order of the graph.
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Graph homomorphisms: structure and symmetry
Geňa Hahn,Claude Tardif +1 more
TL;DR: The first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey can be found in this paper, where the basic definitions, examples and uses of homomorphisms are discussed.
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On the b-Chromatic Number of Graphs
TL;DR: This work determines the asymptotic behavior of b(Gn, p) for the random graph, within the accuracy of a multiplicative factor 2 + o(1) as n ?
References
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Theory of graphs
TL;DR: In this article, the axiom of choice of choice is used to define connectedness path problems in directed graphs and cyclic graphs, as well as Galois correspondences of connectedness paths.