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arXiv · 1907.06936

Graphs with large girth and free groups

Ofir David
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Abstract

We use Margulis' construction together with lattice counting arguments to build Cayley graphs on $\mathrm{SL}_{2}\left(\mathbb{F}_{p}\right),\;p\to\infty$ which are d-regular graphs with girth $\geq\frac{2}{3}\frac{\ln\left(n\right)}{\ln\left(d-1\right)+\ln\left(C\right)}$ for some absolute constant C.

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Ofir David. 2019-07-16. Graphs with large girth and free groups. https://arxiv.org/abs/1907.06936

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