A note on spatial representation of graphs
Jaroslav Nešetřil, Robin D. Thomas (1985)
Commentationes Mathematicae Universitatis Carolinae
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Jaroslav Nešetřil, Robin D. Thomas (1985)
Commentationes Mathematicae Universitatis Carolinae
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I.B. Lackovic, D.M. Cvetkovic (1976)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Izak Broere, Johannes Heidema (2013)
Discussiones Mathematicae Graph Theory
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The well-known Rado graph R is universal in the set of all countable graphs I, since every countable graph is an induced subgraph of R. We study universality in I and, using R, show the existence of 2 א0 pairwise non-isomorphic graphs which are universal in I and denumerably many other universal graphs in I with prescribed attributes. Then we contrast universality for and universality in induced-hereditary properties of graphs and show that the overwhelming majority of induced-hereditary...
Peter Mihók, Jozef Miškuf, Gabriel Semanišin (2009)
Discussiones Mathematicae Graph Theory
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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 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...
Boštjan Brešar, Manoj Changat, Ajitha R. Subhamathi, Aleksandra Tepeh (2010)
Discussiones Mathematicae Graph Theory
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The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are...