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On the dimension of trees |
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| Authors: | Robert C Brigham Ping Zhang |
| Institution: | a Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA b Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA c School of Computer Science, University of Central Florida, Orlando, FL 32816, USA d Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008, USA |
| Abstract: | We consider isometric embedding of trees into the infinite graph Zm whose vertices are the m-dimensional lattice points where two vertices a=(a1,a2,…,am) and b=(b1,b2,…,bm) are adjacent if and only if |ai-bi|?1 for 1?i?m. Linial, London, and Rabinovich have shown that this can be done with  , where t is the number of leaves. In this note, we sketch a proof that  . |
| Keywords: | Isometric embeddings Infinity norm Trees |
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