Universality for and in Induced-Hereditary Graph Properties

Izak Broere ; Johannes Heidema

Discussiones Mathematicae Graph Theory, Tome 33 (2013), p. 33-47 / Harvested from The Polish Digital Mathematics Library

Résumé

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 properties contain no universal graphs. This is made precise by showing that there are 2(2א0 ) properties in the lattice K ≤ of induced-hereditary properties of which only at most 2א0 contain universal graphs. In a final section we discuss the outlook on future work; in particular the question of characterizing those induced-hereditary properties for which there is a universal graph in the property.

Détail

Publié le : 2013-01-01

Zbl 1291.05138

EUDML-ID : urn:eudml:doc:267920

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