{
  "id": "2212.11058",
  "version": "v1",
  "published": "2022-12-21T15:07:22.000Z",
  "updated": "2022-12-21T15:07:22.000Z",
  "title": "Spectrum of $3$-uniform $6$- and $9$-cycle systems over $K_v^{(3)}-I$",
  "authors": [
    "Anita Keszler",
    "Zsolt Tuza"
  ],
  "comment": "45 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if $v\\equiv 0,3,6$ (mod 12) and $v\\geq 6$; and a decomposition into tight 9-cycles exists for all $v\\geq 9$ divisible by 3. These results are complementary to the theorems of Akin et al. [Discrete Math. 345 (2022)] and Bunge et al. [Australas. J. Combin. 80 (2021)].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-21T15:07:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65",
      "05C51",
      "05C38"
    ],
    "keywords": [
      "cycle systems",
      "discrete math",
      "disjoint edges",
      "edge decompositions",
      "parallel class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}