{
  "id": "1811.01477",
  "version": "v1",
  "published": "2018-11-05T01:45:56.000Z",
  "updated": "2018-11-05T01:45:56.000Z",
  "title": "Percolation on the product graph of a regular tree and a line does not satisfy the triangle condition at the uniqueness threshold",
  "authors": [
    "Kohei Yamamoto"
  ],
  "comment": "5 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider Bernoulli bond percolation on the product graph of a regular tree and a line. We show that the triangle condition does not hold at the uniqueness threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T01:45:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangle condition",
      "product graph",
      "regular tree",
      "uniqueness threshold",
      "bernoulli bond percolation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}