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

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".

7 pages, 4 figures. New version has a stronger result and is essentially the accepted version

Cited by in corpus (1)

• A probabilistic approach to exhaustion in the infinite-genus case