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arXiv · 1711.06052

On the critical densities of minor-closed classes

Colin McDiarmid·Michał Przykucki
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Abstract

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

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Colin McDiarmid, Michał Przykucki. 2018-08-02. On the critical densities of minor-closed classes. https://arxiv.org/abs/1711.06052

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