Girth and euclidean distortion

N. Linial, A. Magen, A. Naor

Research output: Contribution to journalArticle

Abstract

Let G be a k-regular graph, k ≥ 3, with girth g. We prove that every embedding f : G → l2 has distortion Ω(√g). Two proofs are given, one based on Markov type [B] and the other on quadratic programming. In the core of both proofs are some Poincaré-type inequalities on graph metrics.

Original languageEnglish (US)
Pages (from-to)380-394
Number of pages15
JournalGeometric and Functional Analysis
Volume12
Issue number2
DOIs
StatePublished - 2002

Fingerprint

Girth
Euclidean
Metric Graphs
Regular Graph
Quadratic Programming

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Girth and euclidean distortion. / Linial, N.; Magen, A.; Naor, A.

In: Geometric and Functional Analysis, Vol. 12, No. 2, 2002, p. 380-394.

Research output: Contribution to journalArticle

Linial, N, Magen, A & Naor, A 2002, 'Girth and euclidean distortion', Geometric and Functional Analysis, vol. 12, no. 2, pp. 380-394. https://doi.org/10.1007/s00039-002-8251-y
Linial, N. ; Magen, A. ; Naor, A. / Girth and euclidean distortion. In: Geometric and Functional Analysis. 2002 ; Vol. 12, No. 2. pp. 380-394.
@article{391b1b959d274b5f919973684ea2a315,
title = "Girth and euclidean distortion",
abstract = "Let G be a k-regular graph, k ≥ 3, with girth g. We prove that every embedding f : G → l2 has distortion Ω(√g). Two proofs are given, one based on Markov type [B] and the other on quadratic programming. In the core of both proofs are some Poincar{\'e}-type inequalities on graph metrics.",
author = "N. Linial and A. Magen and A. Naor",
year = "2002",
doi = "10.1007/s00039-002-8251-y",
language = "English (US)",
volume = "12",
pages = "380--394",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkhauser Verlag Basel",
number = "2",

}

TY - JOUR

T1 - Girth and euclidean distortion

AU - Linial, N.

AU - Magen, A.

AU - Naor, A.

PY - 2002

Y1 - 2002

N2 - Let G be a k-regular graph, k ≥ 3, with girth g. We prove that every embedding f : G → l2 has distortion Ω(√g). Two proofs are given, one based on Markov type [B] and the other on quadratic programming. In the core of both proofs are some Poincaré-type inequalities on graph metrics.

AB - Let G be a k-regular graph, k ≥ 3, with girth g. We prove that every embedding f : G → l2 has distortion Ω(√g). Two proofs are given, one based on Markov type [B] and the other on quadratic programming. In the core of both proofs are some Poincaré-type inequalities on graph metrics.

UR - http://www.scopus.com/inward/record.url?scp=0036435272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036435272&partnerID=8YFLogxK

U2 - 10.1007/s00039-002-8251-y

DO - 10.1007/s00039-002-8251-y

M3 - Article

AN - SCOPUS:0036435272

VL - 12

SP - 380

EP - 394

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 2

ER -