{
  "id": "1909.00214",
  "version": "v1",
  "published": "2019-08-31T13:48:51.000Z",
  "updated": "2019-08-31T13:48:51.000Z",
  "title": "An analogue of the Erdős-Gallai theorem for random graphs",
  "authors": [
    "József Balogh",
    "Andrzej Dudek",
    "Lina Li"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, variants of many classical extremal theorems are proved in random environment. We, complementing existing results, extend the Erd\\H{o}s-Gallai Theorem in random graphs. In particular, we determine, up to a constant factor, the extremal function in $G(N,p)$ for containing a path $P_n$, practically for all values of $N,n$ and $p$. Our work is also motivated by the recent progress on the size-Ramsey number of paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-31T13:48:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graphs",
      "erdős-gallai theorem",
      "size-ramsey number",
      "random environment",
      "classical extremal theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}