{
  "id": "1802.04694",
  "version": "v1",
  "published": "2018-02-13T15:54:52.000Z",
  "updated": "2018-02-13T15:54:52.000Z",
  "title": "A proof of the Bunkbed conjecture on the complete graph for $p\\geqslant1/2$",
  "authors": [
    "Paul de Buyer"
  ],
  "comment": "18 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "The bunkbed of a graph $G$ is the graph $G\\times\\left\\{ 0,1\\right\\} $. It has been conjectured that in the independent bond percolation model, the probability for $\\left(u,0\\right)$ to be connected with $\\left(v,0\\right)$ is greater than the probability for $\\left(u,0\\right)$ to be connected with $\\left(v,1\\right)$, for any vertex $u$, $v$ of $G$. In this article, we prove this conjecture for the complete graph in the case of the independent bond percolation of parameter $p\\geqslant1/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-13T15:54:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B43",
      "60K35"
    ],
    "keywords": [
      "complete graph",
      "bunkbed conjecture",
      "independent bond percolation model",
      "probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}