Graphs and Combinatorics

, Volume 4, Issue 1, pp 43–47 | Cite as

Embedding of trees in euclidean spaces

  • H. Maehara
  • J. Reiterman
  • V. Rödl
  • E. Šiňajová


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.


Euclidean Space Adjacent Vertex Nonadjacent Vertex 
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  1. 1.
    Frankl, P., Maehara, H.: Embedding then-cube in lower dimensions. Europ. J. Comb.7, 221–225 (1986)Google Scholar
  2. 2.
    Frankl, P., Maehara, H.: The Johnson-Lindenstrauss lemma and the sphericity of some graphs. J. Comb. Theory (B) (to appear)Google Scholar
  3. 3.
    Maehara, H.: Space graphs and sphericity. Discrete Appl. Math.49, 55–64 (1984)Google Scholar
  4. 4.
    Maehara, H.: On the sphericity for the join of many graphs. Discrete Math.7, 311–313 (1984)Google Scholar
  5. 5.
    Reiterman, J., Rödl, V., Šiňajová, E.: Geometrical embeddings of graphs. Discrete Math. (to appear)Google Scholar
  6. 6.
    Reiterman, J., Rödl, V., Šiňajová, E.: Embeddings of graphs in Euclidean spaces. Discrete & Computational Geometry (to appear)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • H. Maehara
    • 1
  • J. Reiterman
    • 2
  • V. Rödl
    • 2
  • E. Šiňajová
    • 2
  1. 1.Ryukyu UniversityNishihara, OkinawaJapan
  2. 2.Czech Technical UniversityPraha 1Czechoslovakia

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