{
  "id": "2312.03663",
  "version": "v1",
  "published": "2023-12-06T18:33:00.000Z",
  "updated": "2023-12-06T18:33:00.000Z",
  "title": "$H$-percolation with a random $H$",
  "authors": [
    "Zsolt Bartha",
    "Brett Kolesnik",
    "Gal Kronenberg"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "In $H$-percolation, we start with an Erd\\H{o}s--R\\'enyi graph ${\\mathcal G}_{n,p}$ and then iteratively add edges that complete copies of $H$. The process percolates if all edges missing from ${\\mathcal G}_{n,p}$ are eventually added. We find the critical threshold $p_c$ when $H={\\mathcal G}_{k,1/2}$ is uniformly random, solving a problem of Balogh, Bollob\\'as and Morris.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-06T18:33:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C80",
      "05C99",
      "60K35",
      "68Q80"
    ],
    "keywords": [
      "percolation",
      "iteratively add edges",
      "complete copies",
      "process percolates",
      "critical threshold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}