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arXiv · 0711.3808

Hyperfinite graph limits

Oded Schramm
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Abstract

Gábor Elek introduced the notion of a hyperfinite graph family: a collection of graphs is hypefinite if for every $ε>0$ there is some finite $k$ such that each graph $G$ in the collection can be broken into connected components of size at most $k$ by removing a set of edges of size at most $ε|V(G)|$. We presently extend this notion to a certain compactification of finite bounded-degree graphs, and show that if a sequence of finite graphs converges to a hyperfinite limit, then the sequence itself is hyperfinite.

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Oded Schramm. 2007-11-24. Hyperfinite graph limits. https://arxiv.org/abs/0711.3808

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