{
  "id": "2210.12754",
  "version": "v1",
  "published": "2022-10-23T15:39:53.000Z",
  "updated": "2022-10-23T15:39:53.000Z",
  "title": "Largest subgraph from a hereditary property in a random graph",
  "authors": [
    "Noga Alon",
    "Michael Krivelevich",
    "Wojciech Samotij"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for every non-trivial hereditary family of graphs ${\\cal P}$ and for every fixed $p \\in (0,1)$, the maximum possible number of edges in a subgraph of the random graph $G(n,p)$ which belongs to ${\\cal P}$ is, with high probability, $$ \\left(1-\\frac{1}{k-1}+o(1)\\right)p{n \\choose 2}, $$ where $k$ is the minimum chromatic number of a graph that does not belong to ${\\cal P}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-23T15:39:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C35"
    ],
    "keywords": [
      "random graph",
      "hereditary property",
      "largest subgraph",
      "minimum chromatic number",
      "high probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}