On the separation profile of infinite graphs

Itai Benjamini; Oded Schramm; Ádám Timár

doi:10.4171/GGD/168

On the separation profile of infinite graphs

Itai Benjamini, Oded Schramm, Ádám Timár

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton-Tarjan √n separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.

Original language	English
Pages (from-to)	639-658
Number of pages	20
Journal	Groups Geometry And Dynamics
Volume	6
Issue number	4
DOIs	https://doi.org/10.4171/GGD/168
State	Published - 2012

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Geometry and Topology

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10.4171/GGD/168

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title = "On the separation profile of infinite graphs",

abstract = "Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton-Tarjan √n separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.",

author = "Itai Benjamini and Oded Schramm and {\'A}d{\'a}m Tim{\'a}r",

note = "Swiss NSF [PP0022-118946]; Sinergia grant [CRSI22-130435]; MTA Renyi {"}Lendulet{"} Groups; Renee and Jay Weiss Professorial Chair of Theoretical Mathematics; Graphs Research GroupThe first author was supported by the Renee and Jay Weiss Professorial Chair of Theoretical Mathematics, and the last author by Swiss NSF grants PP0022-118946, Sinergia grant CRSI22-130435 and MTA Renyi {"}Lendulet{"} Groups and Graphs Research Group.",

year = "2012",

doi = "10.4171/GGD/168",

language = "الإنجليزيّة",

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journal = "Groups Geometry And Dynamics",

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AU - Timár, Ádám

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PY - 2012

Y1 - 2012

N2 - Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton-Tarjan √n separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.

AB - Initial steps in the study of inner expansion properties of infinite Cayley graphs and other infinite graphs, such as hyperbolic ones, are taken, in a flavor similar to the well-known Lipton-Tarjan √n separation result for planar graphs. Connections to relaxed versions of quasi-isometries are explored, such as regular and semiregular maps.

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VL - 6

SP - 639

EP - 658

JO - Groups Geometry And Dynamics

JF - Groups Geometry And Dynamics

IS - 4

ER -

On the separation profile of infinite graphs

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