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Graphs and Combinatorics

, Volume 3, Issue 1, pp 39–43 | Cite as

Embedding graphs in Cayley graphs

  • Chris D. Godsil
  • Wilfried Imrich
Article

Abstract

IfY is a finite graph then it is known that every sufficiently large groupG has a Cayley graph containing an induced subgraph isomorphic toY. This raises the question as to what is “sufficiently large”. Babai and Sós have used a probabilistic argument to show that |G| > 9.5 |Y|3 suffices. Using a form of greedy algorithm we strengthen this to\(|G| > (2 + \sqrt 3 )|Y|^3 \). Some related results on finite and infinite groups are included.

Keywords

Greedy Algorithm Related Result Cayley Graph Finite Graph Probabilistic Argument 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Babai, L.: Embedding graphs in Cayley graphs. In: Probl. Comb. Théorie des Graphes (Proc. Conf. Paris-Orsay 1976) edited by J-C. Bermond, et al., pp. 13–15. Paris: C.N.R.S. 1976.Google Scholar
  2. 2.
    Babai, L., Sós, V.T.: Sidon sets in groups and induced subgraphs of Cayley graphs. Europ. J. Comb. (to appear)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Chris D. Godsil
    • 1
  • Wilfried Imrich
    • 2
  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.Institut für Mathematik und Angewandte GeometrieLeobenAustria

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