{
  "id": "2208.10558",
  "version": "v1",
  "published": "2022-08-22T19:23:34.000Z",
  "updated": "2022-08-22T19:23:34.000Z",
  "title": "On the clique number of noisy random geometric graphs",
  "authors": [
    "Matthew Kahle",
    "Minghao Tian",
    "Yusu Wang"
  ],
  "comment": "34 pages, 4 figures",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Let $G_n$ be a random geometric graph, and then for $q,p \\in [0,1)$ we construct a \"$(q,p)$-perturbed noisy random geometric graph\" $G_n^{q,p}$ where each existing edge in $G_n$ is removed with probability $q$, while and each non-existent edge in $G_n$ is inserted with probability $p$. We give asymptotically tight bounds on the clique number $\\omega\\left(G_n^{q,p}\\right)$ for several regimes of parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-22T19:23:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80"
    ],
    "keywords": [
      "clique number",
      "perturbed noisy random geometric graph",
      "non-existent edge",
      "asymptotically tight bounds",
      "probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}