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On Oriented Embedding of the Binary Tree into the Hypercube

Published online by Cambridge University Press:  12 September 2008

Sergej L. Bezrukov
Sergej L. Bezrukov
Affiliation:
Fachbereich Mathematik, Freie Universität Berlin, Arnimallee 2–6, D-14195 Berlin
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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 with l levels into the oriented n-cube as an oriented subgraph, for minimal possible n. A new approach to such problems is presented, which improves the known upper bound n/l ≤ 3/2 given by Havel [1] to n/l ≤ 4/3 + o(1) as l → ∞.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 27 - 38
Copyright
Copyright © Cambridge University Press 1994

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References

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