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⩾3 has largely remained unsolved, even though optimal embeddings (i.e. embeddings achieving minimum δ, λ, and ∈) 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^p, 3^p, 2 ^p*3^q and p, q>0. The embedding of complete ternary trees and the embedding of complete k -ary trees are considered