{
  "id": "1701.05855",
  "version": "v1",
  "published": "2017-01-20T17:00:51.000Z",
  "updated": "2017-01-20T17:00:51.000Z",
  "title": "Judicious partitions of uniform hypergraphs",
  "authors": [
    "John Haslegrave"
  ],
  "journal": "Combinatorica (2014) 34: 561",
  "doi": "10.1007/s00493-014-2916-7",
  "categories": [
    "math.CO"
  ],
  "abstract": "The vertices of any graph with $m$ edges may be partitioned into two parts so that each part meets at least $\\frac{2m}{3}$ edges. Bollob\\'as and Thomason conjectured that the vertices of any $r$-uniform hypergraph with $m$ edges may likewise be partitioned into $r$ classes such that each part meets at least $\\frac{r}{2r-1}m$ edges. In this paper we prove the weaker statement that, for each $r\\ge 4$, a partition into $r$ classes may be found in which each class meets at least $\\frac{r}{3r-4}m$ edges, a substantial improvement on previous bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-20T17:00:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65"
    ],
    "keywords": [
      "uniform hypergraph",
      "judicious partitions",
      "part meets",
      "substantial improvement",
      "class meets"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}