On embedding ternary trees into Boolean hypercubes

It is pointed out that the problem of efficiently embedding a k-ary tree into hypercube with k>or=3 has largely remained unsolved, even though optimal embeddings (i.e. embeddings achieving minimum delta , lambda , and in ) of complete and incomplete binary trees into hypercubes have been known for some time. Thus, in their quest for designing efficient embeddings of k-ary trees into hypercube for arbitrary k, the authors present some preliminary results that give efficient embeddings for the situations when k=3, 2/sup p/, 3/sup p/, 2/sup p/*3/sup q/ and p, q>0. The embedding of complete ternary trees and the embedding of complete k-ary trees are considered.<>