Geodesic
Embedding complete ternary trees into hypercubes
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 463-476

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We inductively describe an embedding of a complete ternary tree Tₕ 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 Tₕ into Q. And it is very close to a conjectured embedding of Havel [3] which states that there exists an embedding of Tₕ into its optimal hypercube with load 1 and dilation 2. The optimal hypercube has dimension ⎡(log₂3)h⎤ ( = ⎡(1.585)h⎤) or ⎡(log₂3)h⎤+1.
Keywords: complete ternary trees, hypercube, interconnection network, embedding, dilation, node congestion, edge congestion 
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Choudum, S.; Lavanya, S. Embedding complete ternary trees into hypercubes. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 3, pp. 463-476. http://geodesic.mathdoc.fr/item/DMGT_2008_28_3_a6/