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On the critical densities of minor-closed classes

Abstract:
Given a minor-closed class A of graphs, let βAdenote the supremum over all graphs in A of the ratio of edges to vertices. We investigate the set B of all such values βA, taking further the project begun by Eppstein. Amongst other results, we determine the small values in B (those up to 2); we show that B is ‘asymptotically dense’; and we answer some questions posed by Eppstein.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.ejc.2018.08.002

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Oxford college:
Corpus Christi College
Role:
Author
Publisher:
Elsevier
Journal:
European Journal of Combinatorics More from this journal
Volume:
75
Pages:
66-91
Publication date:
2018-09-09
Acceptance date:
2018-08-02
DOI:
EISSN:
1095-9971
ISSN:
0195-6698
Pubs id:
pubs:897794
UUID:
uuid:06a7140a-ec24-4efb-bc75-d11a5a11d157
Local pid:
pubs:897794
Source identifiers:
897794
Deposit date:
2018-10-10

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