This is an announcement for the paper "Nonexistence of embeddings with uniformly bounded distortions of Laakso graphs into diamond graphs" by Sofiya Ostrovska and Mikhail I. Ostrovskii.

Abstract: Diamond graphs and Laakso graphs are important examples in the theory of metric embeddings. Many results for these families of graphs are similar to each other. In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. The well-known fact that Laakso graphs are uniformly doubling but diamond graphs are not, immediately implies that diamond graphs do not admit uniformly bilipschitz embeddings into Laakso graphs. The main goal of this paper is to prove that Laakso graphs do not admit uniformly bilipschitz embeddings into diamond graphs.

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

Mathematics Subject Classification: 05C12, 30L05, 46B85

Submitted from: ostrovsm@stjohns.edu

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

http://front.math.ucdavis.edu/1512.06439

or

http://arXiv.org/abs/1512.06439