{
  "id": "2211.06245",
  "version": "v1",
  "published": "2022-11-11T14:36:37.000Z",
  "updated": "2022-11-11T14:36:37.000Z",
  "title": "Cycles as edge intersection hypergraphs of $k$-uniform hypergraphs ($k \\le 6$) -- a constructive approach",
  "authors": [
    "Sophie Pätz",
    "Martin Sonntag"
  ],
  "comment": "17 pages, 10 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "If ${\\cal H}=(V,{\\cal E})$ is a hypergraph, its edge intersection hypergraph $EI({\\cal H})=(V,{\\cal E}^{EI})$ has the edge set ${\\cal E}^{EI}=\\{e_1 \\cap e_2 \\ |\\ e_1, e_2 \\in {\\cal E} \\ \\wedge \\ e_1 \\neq e_2 \\ \\wedge \\ |e_1 \\cap e_2 |\\geq 2\\}$. In the present paper, we consider 4- and 5-uniform hypergraphs ${\\cal H}$, respectively, with $EI({\\cal H}) = C_n$. Our results fill the gap between the 3- and the 6-uniform case considered in arXiv:1902.00396.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-11T14:36:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65"
    ],
    "keywords": [
      "edge intersection hypergraph",
      "uniform hypergraphs",
      "constructive approach",
      "edge set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}