Combinatorica

, Volume 4, Issue 1, pp 53–59

Explicit construction of regular graphs without small cycles

  • Wilfried Imrich
Article

Abstract

For every integerd>2 we give an explicit construction of infinitely many Cayley graphsX of degreed withn(X) vertices and girth >0.4801...(logn(X))/log (d−1)−2. This improves a result of Margulis.

AMS subject classification (1980)

05 C 35 05 C 38 05 C 25 20 E 05 

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References

  1. [1]
    P. Erdős andH. Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl,Wiss. Z. Univ. Halle—Wittenberg, Math.-Nat. R. 12 (1963), 251–258.Google Scholar
  2. [2]
    P. J. Higgings,Categories and Groupoids, Van Nostrand, London, 1971.Google Scholar
  3. [3]
    W. Imrich, Subgroup theorems and graphs,Combinatorial Mathematics, V (Proc. Fifth Austral. Conf. Roy. Melbourne Inst. Techn., Melbourne, 1976), pp. 1–27.Lecture Notes in Math.622, Springer, Berlin, 1977.CrossRefGoogle Scholar
  4. [4]
    W. Magnus, A. Karrass andD. Solitar,Combinatorial group theory, Interscience, N.Y. 1966.MATHGoogle Scholar
  5. [5]
    G. A. Margulis Graphs without short cycles,Combinatorica 2 (1982), 71–78.MATHMathSciNetGoogle Scholar
  6. [6]
    H. Walther, Über reguläre Graphen gegebener Taillenweite und minimaler Knotenzahl,Wiss. Z. HfE Ilmenau 11 (1965), 93–96.MATHMathSciNetGoogle Scholar
  7. [7]
    H. Walther, Eigenschaften von regulären Graphen gegebener Taillenweite und minimaler Knotenzahl,Wiss. Z. HfE Ilmenau 11 (1965), 167–168.MATHMathSciNetGoogle Scholar

Copyright information

© Akadémiai Kiadó 1984

Authors and Affiliations

  • Wilfried Imrich
    • 1
  1. 1.Institut für Mathematik und Angewandte GeometrieLeobenAustria

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