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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1420,
author = {S.A. Choudum and S. Lavanya},
title = {Embedding complete ternary trees into hypercubes},
journal = {Discussiones Mathematicae Graph Theory},
volume = {28},
year = {2008},
pages = {463-476},
zbl = {1173.05013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1420}
}
S.A. Choudum; S. Lavanya. Embedding complete ternary trees into hypercubes. Discussiones Mathematicae Graph Theory, Tome 28 (2008) pp. 463-476. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1420/
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