{
  "id": "2309.00757",
  "version": "v1",
  "published": "2023-09-01T23:07:39.000Z",
  "updated": "2023-09-01T23:07:39.000Z",
  "title": "A Note on Hamiltonian-Intersecting Families of Graphs",
  "authors": [
    "Imre Leader",
    "Žarko Ranđelović",
    "Ta Sheng Tan"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "How many graphs on an $n$-point set can we find such that any two have connected intersection? Berger, Berkowitz, Devlin, Doppelt, Durham, Murthy and Vemuri showed that the maximum is exactly $1/2^{n-1}$ of all graphs. Our aim in this short note is to give a 'directed' version of this result; we show that a family of oriented graphs such that any two have strongly-connected intersection has size at most $1/3^n$ of all oriented graphs. We also show that a family of graphs such that any two have Hamiltonian intersection has size at most $1/2^n$ of all graphs, verifying a conjecture of the above authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-01T23:07:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35"
    ],
    "keywords": [
      "hamiltonian-intersecting families",
      "oriented graphs",
      "point set",
      "short note",
      "hamiltonian intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}