{
  "id": "2301.09910",
  "version": "v1",
  "published": "2023-01-24T10:44:57.000Z",
  "updated": "2023-01-24T10:44:57.000Z",
  "title": "Color-avoiding percolation of random graphs: between the subcritical and the intermediate regime",
  "authors": [
    "Lyuben Lichev"
  ],
  "comment": "8 pages. arXiv admin note: text overlap with arXiv:2211.16086",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Fix a graph $G$ in which every edge is colored in some of $k\\ge 2$ colors. Two vertices $u$ and $v$ are CA-connected if $u$ and $v$ may be connected using any subset of $k - 1$ colors. CA-connectivity is an equivalence relation dividing the vertex set into classes called CA-components. In two recent papers, R\\'ath, Varga, Fekete, and Molontay, and Lichev and Schapira studied the size of the largest CA-component in a randomly colored random graph. The second of these works distinguished and studied three regimes (supercritical, intermediate, and subcritical) in which the largest CA-component has respectively linear, logarithmic, and bounded size. In this short note, we describe the phase transition between the intermediate and the subcritical regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-24T10:44:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "60C05",
      "60K35",
      "82B43"
    ],
    "keywords": [
      "intermediate regime",
      "color-avoiding percolation",
      "subcritical",
      "largest ca-component",
      "equivalence relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}