On the dimension of trees
Abbreviated Journal Title
isometric embeddings; infinity norm; trees; Mathematics
We consider isometric embedding of trees into the infinite graph Z(m) whose vertices are the m-dimensional lattice points where two vertices a = (a(1), a(2),..., a(m)) and b = (b(1), b(2),..., b(m)) are adjacent if and only if vertical bar a(i) - b(i)vertical bar <= 1 for 1 <= i <= m. Linial, London, and Rabinovich have shown that this can be done with m <= 1.7095 log(2) t, where t is the number of leaves. In this note, we sketch a proof that [log(2) t] <= m <= [1.45 log(2) t] (c) 2005 Elsevier B.V. All rights reserved.
"On the dimension of trees" (2005). Faculty Bibliography 2000s. 5012.