On Oriented Embedding of the Binary Tree into the Hypercube

Abstract

We consider the oriented binary tree and the oriented hypercube. The tree edges are oriented from the root to the leaves, while the orientation of the cube edges is induced by the direction from 0 to 1 in the coordinatewise form. The problem is to embed such a tree withllevels into the orientedn-cube as an oriented subgraph, for minimal possiblen. A new approach to such problems is presented, which improves the known upper boundn/l≤ 3/2 given by Havel [1] ton/l≤ 4/3 +o(1) asl→ ∞.