{
  "id": "2205.12246",
  "version": "v1",
  "published": "2022-05-24T17:54:34.000Z",
  "updated": "2022-05-24T17:54:34.000Z",
  "title": "Localized versions of extremal problems",
  "authors": [
    "David Malec",
    "Casey Tompkins"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We generalize several classical theorems in extremal combinatorics by replacing a global constraint with an inequality which holds for all objects in a given class. In particular we obtain generalizations of Tur\\'an's theorem, the Erd\\H{o}s-Gallai theorem, the LYM-inequality, the Erd\\H{o}s-Ko-Rado theorem and the Erd\\H{o}s-Szekeres theorem on sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-24T17:54:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05"
    ],
    "keywords": [
      "extremal problems",
      "localized versions",
      "extremal combinatorics",
      "global constraint",
      "turans theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}