{
  "id": "2012.15142",
  "version": "v1",
  "published": "2020-12-30T13:07:23.000Z",
  "updated": "2020-12-30T13:07:23.000Z",
  "title": "On the Maximum Number of Edges in Hypergraphs with Fixed Matching and Clique Number",
  "authors": [
    "Peter Frankl",
    "Erica L. L. Liu",
    "Jian Wang"
  ],
  "comment": "26 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a $k$-graph $\\mathcal{F}\\subset \\binom{[n]}{k}$, the clique number of $\\mathcal{F}$ is defined to be the maximum size of a subset $Q$ of $[n]$ with $\\binom{Q}{k}\\subset \\mathcal{F}$. In the present paper, we determine the maximum number of edges in a $k$-graph on $[n]$ with matching number at most $s$ and clique number at least $q$ for $n\\geq 8k^2s$ and for $q \\geq (s+1)k-l$, $n\\leq (s+1)k+s/(3k)-l$. Two special cases that $q=(s+1)k-2$ and $k=2$ are solved completely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-30T13:07:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "clique number",
      "maximum number",
      "fixed matching",
      "hypergraphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}