, Volume 4, Issue 1, pp 53-59

First online:

Explicit construction of regular graphs without small cycles

  • Wilfried ImrichAffiliated withInstitut für Mathematik und Angewandte Geometrie

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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