Geodesic
On universal graphs for hom-properties
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 401-409

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A graph property is any isomorphism closed class of simple graphs. For a simple finite graph H, let → H denote the class of all simple countable graphs that admit homomorphisms to H, such classes of graphs are called hom-properties. Given a graph property , a graph G ∈ is universal in if each member of is isomorphic to an induced subgraph of G. In particular, we consider universal graphs in → H and we give a new proof of the existence of a universal graph in → H, for any finite graph H.
Keywords: universal graph, weakly universal graph, hom-property, core 
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Mihók, Peter; Miškuf, Jozef; Semanišin, Gabriel. On universal graphs for hom-properties. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 401-409. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a13/