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Graph homomorphisms: Structure and symmetry. (English) Zbl 0880.05079
Hahn, Geňa (ed.) et al., Graph symmetry: algebraic methods and applications. Proceedings of the NATO Advanced Study Institute and séminaire de mathématiques supérieures, Montréal, Canada, July 1-12, 1996. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 497, 107-166 (1997).
As the authors write, this paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. To inform a reader about this paper it will be suitable to list its chapters and topics. It has six chapters. The first chapter is “Introduction”. The second chapter “Basics” has the following items: Basic definitions, Quotients, Retracts, Cores, Homomorphic equivalence, Products. The third chapter “Vertex-transitive graphs” has the themes: Cayley graphs, Independence ratio and the no-homomorphism lemma, Cores of vertex-transitive graphs, Kneser graphs, Circular graphs. The fourt chapter “Graph colourings and variations” has the subjects: Chromatic number, Achromatic number, Kneser colourings, Circular colourings, Fractional chromatic number, Chromatic difference sequence, Ultimate independence ratio. The fifth chapter “Graph products” has the sections: The categorial product and Hedetniemi’s conjecture, The Cartesian product and normal Cayley graphs, The strong product and the lexicographic product, Isometric embeddings and retracts. The sixth chapter is very short and is called “Remarks”.
For the entire collection see [Zbl 0868.00039].

MSC:
05C99 Graph theory
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
05C15 Coloring of graphs and hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
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