{
  "id": "2404.11268",
  "version": "v1",
  "published": "2024-04-17T11:20:13.000Z",
  "updated": "2024-04-17T11:20:13.000Z",
  "title": "The maximum number of cliques in graphs with given fractional matching number and minimum degree",
  "authors": [
    "Chengli Li",
    "Yurui Tang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Recently, Ma, Qian and Shi determined the maximum size of an $n$-vertex graph with given fractional matching number $s$ and maximum degree at most $d$. Motivated by this result, we determine the maximum number of $\\ell$-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma's result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-17T11:20:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum degree",
      "maximum number",
      "complete bipartite graphs",
      "maximum size",
      "prescribed fractional matching number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}