Year: 2007
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Schramm, Oded
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394659135