It is proved that for any treeT the vertices ofT can be placed on the surface of a sphere inR3 in such a way that adjacent vertices have distance 1 and nonadjacent vertices have distances less than 1.
KeywordsEuclidean Space Adjacent Vertex Nonadjacent Vertex
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- 1.Frankl, P., Maehara, H.: Embedding then-cube in lower dimensions. Europ. J. Comb.7, 221–225 (1986)Google Scholar
- 2.Frankl, P., Maehara, H.: The Johnson-Lindenstrauss lemma and the sphericity of some graphs. J. Comb. Theory (B) (to appear)Google Scholar
- 3.Maehara, H.: Space graphs and sphericity. Discrete Appl. Math.49, 55–64 (1984)Google Scholar
- 4.Maehara, H.: On the sphericity for the join of many graphs. Discrete Math.7, 311–313 (1984)Google Scholar
- 5.Reiterman, J., Rödl, V., Šiňajová, E.: Geometrical embeddings of graphs. Discrete Math. (to appear)Google Scholar
- 6.Reiterman, J., Rödl, V., Šiňajová, E.: Embeddings of graphs in Euclidean spaces. Discrete & Computational Geometry (to appear)Google Scholar