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Subcritical Graph Classes Containing All Planar Graphs

Part of: Graph theory Combinatorics

Published online by Cambridge University Press:  22 March 2018

AGELOS GEORGAKOPOULOS  and
STEPHAN WAGNER
AGELOS GEORGAKOPOULOS
Affiliation:
Mathematics Institute, University of Warwick, CV4 7AL, UK
STEPHAN WAGNER
Affiliation:
Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa (e-mail: swagner@sun.ac.za)
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Abstract

We construct minor-closed addable families of graphs that are subcritical and contain all planar graphs. This contradicts (one direction of) a well-known conjecture of Noy.

MSC classification

Primary: 05C30: Enumeration in graph theory
Secondary: 05A16: Asymptotic enumeration 05C10: Planar graphs; geometric and topological aspects of graph theory 05C80: Random graphs 05C83: Graph minors

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 5 , September 2018 , pp. 763 - 773
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†

Supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 639046).

‡

Supported by the National Research Foundation of South Africa, grant number 96236.

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