{
  "id": "1910.11225",
  "version": "v1",
  "published": "2019-10-24T15:27:31.000Z",
  "updated": "2019-10-24T15:27:31.000Z",
  "title": "Localization Game for Random Graphs",
  "authors": [
    "Andrzej Dudek",
    "Sean English",
    "Alan Frieze",
    "Calum MacRury",
    "Pawel Pralat"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider the localization game played on graphs in which a cop tries to determine the exact location of an invisible robber by exploiting distance probes. The corresponding graph parameter $\\zeta(G)$ for a given graph $G$ is called the localization number. In this paper, we improve the bounds for dense random graphs determining an asymptotic behaviour of $\\zeta(G)$. Moreover, we extend the argument to sparse graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-24T15:27:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "localization game",
      "dense random graphs determining",
      "sparse graphs",
      "exact location",
      "localization number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}