# On the isoperimetry of graphs with many ends

Colloquium Mathematicae (1998)

- Volume: 78, Issue: 2, page 307-318
- ISSN: 0010-1354

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topPittet, Christophe. "On the isoperimetry of graphs with many ends." Colloquium Mathematicae 78.2 (1998): 307-318. <http://eudml.org/doc/210617>.

@article{Pittet1998,

abstract = {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.)},

author = {Pittet, Christophe},

journal = {Colloquium Mathematicae},

keywords = {cohomology; connected graph; radius; isoperimetric inequality; Cayley graph; ends},

language = {eng},

number = {2},

pages = {307-318},

title = {On the isoperimetry of graphs with many ends},

url = {http://eudml.org/doc/210617},

volume = {78},

year = {1998},

}

TY - JOUR

AU - Pittet, Christophe

TI - On the isoperimetry of graphs with many ends

JO - Colloquium Mathematicae

PY - 1998

VL - 78

IS - 2

SP - 307

EP - 318

AB - 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.)

LA - eng

KW - cohomology; connected graph; radius; isoperimetric inequality; Cayley graph; ends

UR - http://eudml.org/doc/210617

ER -

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