{
  "id": "1802.04586",
  "version": "v1",
  "published": "2018-02-13T12:29:47.000Z",
  "updated": "2018-02-13T12:29:47.000Z",
  "title": "Hamiltonicity in randomly perturbed hypergraphs",
  "authors": [
    "Jie Han",
    "Yi Zhao"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For integers $k\\ge 3$ and $1\\le \\ell\\le k-1$, we prove that for any $\\alpha>0$, there exist $\\epsilon>0$ and $C>0$ such that for sufficiently large $n\\in (k-\\ell)\\mathbb{N}$, the union of a $k$-uniform hypergraph with minimum vertex degree $\\alpha n^{k-1}$ and a binomial random $k$-uniform hypergraph $\\mathbb{G}^{(k)}(n,p)$ with $p\\ge n^{-(k-\\ell)-\\epsilon}$ for $\\ell\\ge 2$ and $p\\ge C n^{-(k-1)}$ for $\\ell=1$ on the same vertex set contains a Hamiltonian $\\ell$-cycle with high probability. Our result is best possible up to the values of $\\epsilon$ and $C$ and answers a question of Krivelevich, Kwan and Sudakov.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-13T12:29:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "05C45"
    ],
    "keywords": [
      "randomly perturbed hypergraphs",
      "hamiltonicity",
      "uniform hypergraph",
      "minimum vertex degree",
      "vertex set contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}