{
  "id": "1503.06346",
  "version": "v1",
  "published": "2015-03-21T20:07:03.000Z",
  "updated": "2015-03-21T20:07:03.000Z",
  "title": "Jigsaw Percolation on Erdos-Renyi Random Graphs",
  "authors": [
    "Erik Slivken"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We extend the jigsaw percolation model to analyze graphs where both underlying people and puzzle graphs are Erd\\H{o}s-R\\'{e}nyi random graphs. Let $p_{\\text{ppl}}$ and $p_{\\text{puz}}$ denote the probability that an edge exists in the respective people and puzzle graphs and define $p_{\\text{eff}}= p_{\\text{ppl}}p_{\\text{puz}}$, the effective probability. We show for constants $c_1>1$ and $c_2> \\pi^2/6$ and $c_3<e^{-5}$ if $min(p_{\\text{ppl}},p_{\\text{puz}}) > c_1 \\log n /n$ the critical effective probability $p^c_{\\text{eff}}$, satisfies $c_3 < p^c_{\\text{eff}}n\\log n < c_2.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-21T20:07:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G99"
    ],
    "keywords": [
      "erdos-renyi random graphs",
      "puzzle graphs",
      "effective probability",
      "jigsaw percolation model",
      "analyze graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}