Low-distortion embeddings of graphs with large girth
  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). 
Mikhail I. Ostrovskii
math.MG math.CO math.FA