Nonexistence of embeddings with uniformly bounded distortions of Laakso graphs into diamond graphs

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• 作者：Sofiya Ostrovska^a ; ^{sofia.ostrovska@atilim.edu.tr} ; Mikhail I. Ostrovskii^b ; ^{ostrovsm@stjohns.edu}
• 关键词：Diamond graphs ; Doubling metric space ; Laakso space ; Lipschitz map
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 February 2017
• 年：2017
• 卷：340
• 期：2
• 页码：9-17
• 全文大小：427 K
• 卷排序：340

文摘

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.