This is an announcement for the paper "Low-distortion embeddings of graphs with large girth" by Mikhail I. Ostrovskii.

Abstract: The main purpose of the paper is to construct a sequence of graphs of constant degree with indefinitely growing girths admitting embeddings into $\ell_1$ with uniformly bounded distortions. This result answers the problem posed by N.~Linial, A.~Magen, and A.~Naor (2002).

Archive classification: math.MG math.CO math.FA

Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12, 54E35

Submitted from: ostrovsm@stjohns.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1108.2542

or

http://arXiv.org/abs/1108.2542