{
  "id": "1606.05616",
  "version": "v1",
  "published": "2016-06-17T18:21:24.000Z",
  "updated": "2016-06-17T18:21:24.000Z",
  "title": "The minimum vertex degree for an almost-spanning tight cycle in a $3$-uniform hypergraph",
  "authors": [
    "Oliver Cooley",
    "Richard Mycroft"
  ],
  "comment": "10 pages. arXiv admin note: text overlap with arXiv:1411.4957",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\\left(\\frac{5}{9} + o(1) \\right)\\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, B\\\"ottcher, Cooley and Mycroft.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-17T18:21:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum vertex degree",
      "almost-spanning tight cycle",
      "uniform hypergraph",
      "hypergraph regularity method",
      "hypergraph regularity lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}