{
  "id": "2002.03189",
  "version": "v1",
  "published": "2020-02-08T15:41:26.000Z",
  "updated": "2020-02-08T15:41:26.000Z",
  "title": "Maximizing the number of independent sets of fixed size in $K_n$-covered graphs",
  "authors": [
    "Anyao Wang",
    "Xinmin Hou",
    "Boyuan Liu",
    "Yue Ma"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph $G$ is $H$-covered by some given graph $H$ if each vertex in $G$ is contained in a copy of $H$. In this note, we give the maximum number of independent sets of size $t\\ge 3$ in $K_n$-covered graphs of size $N\\ge n+t-1$ and determine its extremal graph. The result answers a question proposed by Chakraborit and Loh. The proof uses an edge-switching operation of hypergraphs which remains the number of independent sets nondecreasing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-08T15:41:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "05C69"
    ],
    "keywords": [
      "covered graphs",
      "fixed size",
      "maximum number",
      "maximizing",
      "extremal graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}