{
  "id": "1907.06936",
  "version": "v1",
  "published": "2019-07-16T10:59:19.000Z",
  "updated": "2019-07-16T10:59:19.000Z",
  "title": "Graphs with large girth and free groups",
  "authors": [
    "Ofir David"
  ],
  "comment": "3 figures, 14 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-16T10:59:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "20E05",
      "14H30"
    ],
    "keywords": [
      "free groups",
      "large girth",
      "build cayley graphs",
      "absolute constant",
      "d-regular graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}