{
  "id": "2004.11828",
  "version": "v1",
  "published": "2020-04-24T16:09:53.000Z",
  "updated": "2020-04-24T16:09:53.000Z",
  "title": "A note on a stability result for the Fano plane",
  "authors": [
    "Carlos Hoppen",
    "Hanno Lefmann",
    "Knut Odermann"
  ],
  "comment": "This article has been posted to give support to results about edge-coloring of 3-uniform hypergraphs that do not contain a copy of the Fano plane",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note, we adapt the Keevash-Sudakov proof of the (Tur\\'{a}n) Stability Theorem for the Fano plane to find an explicit dependency between the parameters $\\varepsilon$ and $\\delta$. This is useful in the solution of a multicolored version for hypergraphs of an extremal problem about edge-colorings, known as the Erd\\H{o}s-Rothschild problem, which may be considered for the Fano plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-24T16:09:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fano plane",
      "stability result",
      "stability theorem",
      "explicit dependency",
      "extremal problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}