{
  "id": "1810.01731",
  "version": "v1",
  "published": "2018-10-03T13:33:05.000Z",
  "updated": "2018-10-03T13:33:05.000Z",
  "title": "Judiciously 3-partitioning 3-uniform hypergraphs",
  "authors": [
    "Hunter Spink",
    "Marius Tiba"
  ],
  "comment": "18 pages, comments welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "Bollob\\'as, Reed and Thomason proved every $3$-uniform hypergraph $\\mathcal{H}$ with $m$ edges has a vertex-partition $V(\\mathcal{H})=V_1 \\sqcup V_2 \\sqcup V_3$ such that each part meets at least $\\frac{1}{3}(1-\\frac{1}{e})m$ edges, later improved to $0.6m$ by Halsegrave and improved asymptotically to $0.65m+o(m)$ by Ma and Yu. We improve this asymptotic bound to $\\frac{19}{27}m+o(m)$, which is best possible up to the error term, resolving a special case of a conjecture of Bollob\\'as and Scott.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-03T13:33:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65"
    ],
    "keywords": [
      "uniform hypergraph",
      "part meets",
      "asymptotic bound",
      "error term",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}