{
  "id": "2212.14516",
  "version": "v1",
  "published": "2022-12-30T02:05:08.000Z",
  "updated": "2022-12-30T02:05:08.000Z",
  "title": "A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs",
  "authors": [
    "Alexandr Kostochka",
    "Ruth Luo",
    "Grace McCourt"
  ],
  "comment": "22 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Dirac proved that each $n$-vertex $2$-connected graph with minimum degree at least $k$ contains a cycle of length at least $\\min\\{2k, n\\}$. We prove a hypergraph version of this result: for $n \\geq k \\geq r+2 \\geq 5$, every $2$-connected $r$-uniform $n$-vertex hypergraph with minimum degree at least ${k-1 \\choose r-1} + 1$ has a Berge cycle of length at least $\\min\\{2k, n\\}$. The bound is exact for all $k\\geq r+2\\geq 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-30T02:05:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C65",
      "05C38",
      "05C35"
    ],
    "keywords": [
      "long cycles",
      "diracs theorem",
      "hypergraph analog",
      "minimum degree",
      "berge cycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}