Embedding of trees in euclidean spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1988 English Publisher:Springer Science and Business Media LLCJournal:Graphs and Combinatorics, volume 4, pages 43-47 (issn: 0911-0119, eissn: 1435-5914,

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Authors: Hiroshi Maehara; Jan Reiterman; Vojtech Rödl; Edita Sinajová;

doi: 10.1007/bf01864152

Embedding of trees in euclidean spaces

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Abstract

It is proved that for any tree T the vertices of T can be placed on the surface of a sphere in \(R^ 3\) in such a way that adjacent vertices have distance 1 and nonadjacent vertices have distance less than 1. This improves an earlier result of the last three authors (to appear in Discrete and Computational Geometry).

Related Organizations

Czech Technical University in Prague
Czech Republic
University of the Ryukyus University Hospital
Japan

Keywords

embedding in a sphere, Euclidean geometries (general) and generalizations, Trees, Planar graphs; geometric and topological aspects of graph theory, tree

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