{
  "id": "2308.07608",
  "version": "v1",
  "published": "2023-08-15T07:34:12.000Z",
  "updated": "2023-08-15T07:34:12.000Z",
  "title": "Extremal problems for disjoint graphs",
  "authors": [
    "Zhenyu Ni",
    "Jing Wang",
    "Liying Kang"
  ],
  "comment": "23 pages. arXiv admin note: text overlap with arXiv:2306.16747",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a simple graph $F$, let $\\mathrm{EX}(n, F)$ and $\\mathrm{EX_{sp}}(n,F)$ be the set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an $n$-vertex graph without any copy of the graph $F$, respectively. Let $F$ be a graph with $\\mathrm{ex}(n,F)=e(T_{n,r})+O(1)$. In this paper, we show that $\\mathrm{EX_{sp}}(n,kF)\\subseteq \\mathrm{EX}(n,kF)$ for sufficiently large $n$. This generalizes a result of Wang, Kang and Xue [J. Comb. Theory, Ser. B, 159(2023) 20-41]. We also determine the extremal graphs of $kF$ in term of the extremal graphs of $F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-15T07:34:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C35"
    ],
    "keywords": [
      "disjoint graphs",
      "extremal problems",
      "extremal graphs",
      "maximum spectral radius",
      "maximum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}