On the critical densities of minor-closed classes

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  • University of Oxford


Given a minor-closed class A of graphs, let β A denote the supremum over all graphs in A of the ratio of edges to vertices. We investigate the set B of all such values β A, 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.


Original languageEnglish
Pages (from-to)66-91
Number of pages26
JournalEuropean Journal of Combinatorics
Early online date9 Sep 2018
Publication statusPublished - 1 Jan 2019