{
  "id": "2101.12205",
  "version": "v1",
  "published": "2021-01-28T18:59:20.000Z",
  "updated": "2021-01-28T18:59:20.000Z",
  "title": "Cycle decompositions in $3$-uniform hypergraphs",
  "authors": [
    "Simón Piga",
    "Nicolás Sanhueza-Matamala"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that $3$-graphs whose codegree is at least $(2/3 + o(1))n$ can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing that our bounds are best possible up to the $o(1)$ term. All together, our results answer in the negative some recent questions of Glock, Joos, K\\\"uhn, and Osthus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-28T18:59:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "05C45",
      "05C70"
    ],
    "keywords": [
      "uniform hypergraphs",
      "cycle decompositions",
      "trivial necessary divisibility conditions",
      "admit euler tours",
      "tight cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}