# Universality for and in Induced-Hereditary Graph Properties

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 1, page 33-47
- ISSN: 2083-5892

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topIzak Broere, and Johannes Heidema. "Universality for and in Induced-Hereditary Graph Properties." Discussiones Mathematicae Graph Theory 33.1 (2013): 33-47. <http://eudml.org/doc/267920>.

@article{IzakBroere2013,

abstract = {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.},

author = {Izak Broere, Johannes Heidema},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {countable graph; universal graph; induced-hereditary property},

language = {eng},

number = {1},

pages = {33-47},

title = {Universality for and in Induced-Hereditary Graph Properties},

url = {http://eudml.org/doc/267920},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Izak Broere

AU - Johannes Heidema

TI - Universality for and in Induced-Hereditary Graph Properties

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 1

SP - 33

EP - 47

AB - 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.

LA - eng

KW - countable graph; universal graph; induced-hereditary property

UR - http://eudml.org/doc/267920

ER -

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