{
  "id": "1906.05639",
  "version": "v1",
  "published": "2019-06-13T12:51:54.000Z",
  "updated": "2019-06-13T12:51:54.000Z",
  "title": "Nearly all cacti are edge intersection hypergraphs of 3-uniform hypergraphs",
  "authors": [
    "Martin Sonntag",
    "Hanns-Martin Teichert"
  ],
  "comment": "9 pages, 3 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 ${\\cal E}^{EI}=\\{e_1 \\cap e_2 \\ |\\ e_1, e_2 \\in {\\cal E} \\ \\wedge \\ e_1 \\neq e_2 \\ \\wedge \\ |e_1 \\cap e_2 |\\geq2\\}$. Using the so-called clique-fusion, we show that nearly all cacti are edge intersection hypergraphs of 3-uniform hypergraphs. In the proof we make use of known characterizations of the trees and the cycles which are edge intersection hypergraphs of 3-uniform hypergraphs (see arXiv:1901.06292).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-13T12:51:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65"
    ],
    "keywords": [
      "edge intersection hypergraph",
      "edge set",
      "clique-fusion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}