The random graph embeds in the curve graph of any infinite genus surface

Edgar A. Bering IV; Jonah Gaster

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arXiv · 1405.6423

The random graph embeds in the curve graph of any infinite genus surface

Edgar A. Bering IV·Jonah Gaster

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Abstract

The random graph is an infinite graph with the universal property that any embedding of $G-v$ extends to an embedding of $G$, for any finite graph. In this paper we show that this graph embeds in the curve graph of a surface $\Sigma$ if and only if $\Sigma$ has infinite genus, showing that the curve system on an infinite genus surface is "as complicated as possible".

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BibTeX RIS

Edgar A. Bering IV, Jonah Gaster. 2014-05-25. The random graph embeds in the curve graph of any infinite genus surface. https://arxiv.org/abs/1405.6423

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