Explicit construction of regular graphs without small cycles

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.

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Dedicated to Paul Erdős on his seventieth birthday

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Imrich, W. Explicit construction of regular graphs without small cycles. Combinatorica 4, 53–59 (1984). https://doi.org/10.1007/BF02579157

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 38
  • 05 C 25
  • 20 E 05