### Abstract

In this paper we partially prove a conjecture that was raised by Linial, London and Rabinovich in [11]. Let G be a k-regular graph, k ≥ 3, with girth g. We show that every embedding f : G → ℓ_{2} has distortion Ω(√g). The original conjecture which remains open is that the Euclidean distortion is bounded below by Ω(g). Two proofs are given, one based on semi-definite programming, and the other on Markov Type, a concept that considers random walks on metrics.

Original language | English (US) |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Pages | 705-711 |

Number of pages | 7 |

State | Published - 2002 |

Event | Proceedings of the 34th Annual ACM Symposium on Theory of Computing - Montreal, Que., Canada Duration: May 19 2002 → May 21 2002 |

### Other

Other | Proceedings of the 34th Annual ACM Symposium on Theory of Computing |
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Country | Canada |

City | Montreal, Que. |

Period | 5/19/02 → 5/21/02 |

### ASJC Scopus subject areas

- Software

## Cite this

Linial, N., Magen, A., & Naor, A. (2002). Girth and Euclidean distortion. In

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 705-711)