Geodesic
On the isoperimetry of graphs with many ends
Colloquium Mathematicum, Tome 78 (1998) no. 2, pp. 307-318.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let X be a connected graph with uniformly bounded degree. We show that if there is a radius r such that, by removing from X any ball of radius r, we get at least three unbounded connected components, then X satisfies a strong isoperimetric inequality. In particular, the non-reduced $l^2$-cohomology of X coincides with the reduced $l^2$-cohomology of X and is of uncountable dimension. (Those facts are well known when X is the Cayley graph of a finitely generated group with infinitely many ends.)
DOI : 10.4064/cm-78-2-307-318

Christophe Pittet 1

1 
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Christophe Pittet. On the isoperimetry of graphs with many ends. Colloquium Mathematicum, Tome 78 (1998) no. 2, pp. 307-318. doi : 10.4064/cm-78-2-307-318. http://geodesic.mathdoc.fr/articles/10.4064/cm-78-2-307-318/

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