{
  "id": "2003.12701",
  "version": "v1",
  "published": "2020-03-28T04:18:11.000Z",
  "updated": "2020-03-28T04:18:11.000Z",
  "title": "Extremal graphs of the $k$-th power of paths",
  "authors": [
    "Long-Tu Yuan"
  ],
  "comment": "9pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "An extremal graph for a given graph $H$ is a graph with maximum number of edges on fixed number of vertices without containing a copy of $H$. The $k$-th power of a path is a graph obtained from a path and joining all pair of vertices of the path with distance less than $k$. Applying a deep theorem of Simonovits, we characterize the extremal graphs of the $k$-th power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-28T04:18:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "extremal graph",
      "th power",
      "maximum number",
      "stronger form",
      "deep theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}