Embedding binary trees and caterpillars into the hypercube

Abstract

Embedding graphs is an important and well-studied theory in parallel computing. Finding the embedding of trees into hypercubes is an important, interesting and difficult problem. This work studies the embedding of binary trees and caterpillars into hypercubes. We give an embedding for a special type of binary tree into its optimal hypercube. We also present embedding of generalized ladders as subgraph into the hypercube. Through an embedding of caterpillars into generalized ladders, we have obtained an embedding of a class of caterpillars into their optimal hypercube.