{
  "id": "2109.01536",
  "version": "v1",
  "published": "2021-09-03T14:01:02.000Z",
  "updated": "2021-09-03T14:01:02.000Z",
  "title": "Extremal problems of double stars",
  "authors": [
    "Ervin Győri",
    "Runze Wang",
    "Spencer Woolfson"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In a generalized Tur\\'an problem, two graphs $H$ and $F$ are given and the question is the maximum number of copies of $H$ in an $F$-free graph of order $n$. In this paper, we study the number of double stars $S_{k,l}$ in triangle-free graphs. We also study an opposite version of this question: what is the maximum number edges/triangles in graphs with double star type restrictions, which leads us to study two questions related to the extremal number of triangles or edges in graphs with degree-sum constraints over adjacent or non-adjacent vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-03T14:01:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "extremal problems",
      "maximum number edges/triangles",
      "double star type restrictions",
      "non-adjacent vertices",
      "generalized turan problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}