Discussiones Mathematicae Graph Theory 29(2) (2009)
401-409
DOI: https://doi.org/10.7151/dmgt.1455
ON UNIVERSAL GRAPHS FOR HOM-PROPERTIES
Peter Mihók
Department of Applied Mathematics | Jozef Miskuf
Institute of Mathematics | Gabriel Semanišin
Institute of Computer Science |
Abstract
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 P, a graph G ∈ P is universal in P if each member of P 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.
2000 Mathematics Subject Classification: 05C15, 05C75.
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Received 20 January 2008
Revised 8 July 2009
Accepted 8 July 2009
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