{
  "id": "1608.04675",
  "version": "v1",
  "published": "2016-08-16T17:12:49.000Z",
  "updated": "2016-08-16T17:12:49.000Z",
  "title": "A Stability Theorem for Maximal $K_{r+1}$-free Graphs",
  "authors": [
    "Kamil Popielarz",
    "Julian Sahasrabudhe",
    "Richard Snyder"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For $r \\geq 2$, we show that every maximal $K_{r+1}$-free graph $G$ on $n$ vertices with $(1-\\frac{1}{r})\\frac{n^2}{2}-o(n^{\\frac{r+1}{r}})$ edges contains a complete $r$-partite subgraph on $(1 - o(1))n$ vertices. We also show that this is best possible. This result answers a question of Tyomkyn and Uzzell.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-16T17:12:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "free graph",
      "stability theorem",
      "edges contains",
      "partite subgraph",
      "result answers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}