Graphs with large girth and free groups

2019/07/16 by David, Ofir
#05C25 20E05 14H30 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1907.06936

Abstract

We use Margulis' construction together with lattice counting arguments to build Cayley graphs on SL₂(\mathbbF_p), p→∞ which are d-regular graphs with girth ≥(2)/(3)(ln(n))/(ln(d-1)+ln(C)) for some absolute constant C.

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