Universality for and in Induced-Hereditary Graph Properties

• Autorzy: Izak Broere , Johannes Heidema
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

countable graph; universal graph; induced-hereditary property

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 1
• Strony: 33-47

Daty

wydano

2013-03-01

online

2013-04-13

Twórcy

autor

Izak Broere

• Department of Mathematics and Applied Mathematics University of Pretoria

autor

Johannes Heidema

• Department of Mathematical Sciences University of South Africa

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1671