{
  "id": "2101.03223",
  "version": "v1",
  "published": "2021-01-08T21:13:43.000Z",
  "updated": "2021-01-08T21:13:43.000Z",
  "title": "A note on stability for maximal $F$-free graphs",
  "authors": [
    "Dániel Gerbner"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Popielarz, Sahasrabudhe and Snyder in 2018 proved that maximal $K_{r+1}$-free graphs with $(1-\\frac{1}{r})\\frac{n^2}{2}-o(n^{\\frac{r+1}{r}})$ edges contain a complete $r$-partite subgraph on $n-o(n)$ vertices. This was very recently extended to odd cycles in place of $K_3$ by Wang, Wang, Yang and Yuan. We further extend it to some other 3-chromatic graphs, and obtain some other stability results along the way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-08T21:13:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graphs",
      "stability results",
      "odd cycles",
      "partite subgraph",
      "edges contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}