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Dense sets and embedding binary trees into hypercubes. (English) Zbl 1111.05023
Summary: The purpose of this paper is to describe a method for embedding binary trees into hypercubes based on an iterative embedding into their subgraphs induced by dense sets. As a particular application, we present a class of binary trees, defined in terms of size of their subtrees, whose members allow a dilation two embedding into their optimal hypercubes. This provides a partial evidence in favor of a long-standing conjecture of Bhatt and Ipsen which claims that such an embedding exists for an arbitrary binary tree.

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C05 Trees
68M07 Mathematical problems of computer architecture
68R10 Graph theory (including graph drawing) in computer science
Software:
IPSEN
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References:
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