New York Journal of Mathematics
Volume 23 (2017) 59-66


Edgar A. Bering IV and Jonah Gaster

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

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Published: January 9, 2017
Keywords: Random graph, curve graph, stability
Subject: Primary: 57M15

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 Σ if and only if Σ has infinite genus, showing that the curve system on an infinite genus surface is "as complicated as possible''.

Author information

Edgar A. Bering IV:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S Morgan St. (M/C 249), Chicago, IL, 60607

Jonah Gaster:
Department of Mathematics, Boston College, Chestnut Hill, MA 02467