{
  "id": "1401.5678",
  "version": "v2",
  "published": "2014-01-22T14:12:08.000Z",
  "updated": "2014-06-11T13:04:12.000Z",
  "title": "On the hyperbolicity of random graphs",
  "authors": [
    "Dieter Mitche",
    "Pawel Pralat"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V,E)$ be a connected graph with the usual (graph) distance metric $d:V \\times V \\to N \\cup \\{0 \\}$. Introduced by Gromov, $G$ is $\\delta$-hyperbolic if for every four vertices $u,v,x,y \\in V$, the two largest values of the three sums $d(u,v)+d(x,y), d(u,x)+d(v,y), d(u,y)+d(v,x)$ differ by at most $2\\delta$. In this paper, we determinate the value of this hyperbolicity for most binomial random graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-11T13:04:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolicity",
      "binomial random graphs",
      "largest values",
      "distance metric",
      "connected graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5678M"
    }
  }
}