# Universality in Graph Properties with Degree Restrictions

Izak Broere; Johannes Heidema; Peter Mihók

Discussiones Mathematicae Graph Theory (2013)

- Volume: 33, Issue: 3, page 477-492
- ISSN: 2083-5892

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topIzak Broere, Johannes Heidema, and Peter Mihók. "Universality in Graph Properties with Degree Restrictions." Discussiones Mathematicae Graph Theory 33.3 (2013): 477-492. <http://eudml.org/doc/268159>.

@article{IzakBroere2013,

abstract = {Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set [...] of all countable graphs (since every graph in [...] is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of [...] is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.},

author = {Izak Broere, Johannes Heidema, Peter Mihók},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {countable graph; universal graph; induced-hereditary; k-degenerate graph; graph with colouring number at most k + 1; graph property with assignment; -degenerate graph; graph with colouring number at most },

language = {eng},

number = {3},

pages = {477-492},

title = {Universality in Graph Properties with Degree Restrictions},

url = {http://eudml.org/doc/268159},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Izak Broere

AU - Johannes Heidema

AU - Peter Mihók

TI - Universality in Graph Properties with Degree Restrictions

JO - Discussiones Mathematicae Graph Theory

PY - 2013

VL - 33

IS - 3

SP - 477

EP - 492

AB - Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in the m’th position of its binary expansion. It is well known that R is a universal graph in the set [...] of all countable graphs (since every graph in [...] is isomorphic to an induced subgraph of R). A brief overview of known universality results for some induced-hereditary subsets of [...] is provided. We then construct a k-degenerate graph which is universal for the induced-hereditary property of finite k-degenerate graphs. In order to attempt the corresponding problem for the property of countable graphs with colouring number at most k + 1, the notion of a property with assignment is introduced and studied. Using this notion, we are able to construct a universal graph in this graph property and investigate its attributes.

LA - eng

KW - countable graph; universal graph; induced-hereditary; k-degenerate graph; graph with colouring number at most k + 1; graph property with assignment; -degenerate graph; graph with colouring number at most

UR - http://eudml.org/doc/268159

ER -

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