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We inductively describe an embedding of a complete ternary tree T h of height h into a hypercube Q of dimension at most (1.6)h + 1 with load 1, dilation 2, node congestion 2 and edge congestion 2. This is an improvement over the known embedding of T h into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of T h into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension (log 2 3)h (= (1.585)h) or (log 2 3)h + 1.

Embedding complete ternary trees into hypercubes