{
  "id": "1303.5022",
  "version": "v4",
  "published": "2013-03-20T18:38:10.000Z",
  "updated": "2014-02-24T18:38:04.000Z",
  "title": "Turán Numbers for Forests of Paths in Hypergraphs",
  "authors": [
    "Neal Bushaw",
    "Nathan Kettle"
  ],
  "comment": "Referee suggestions incorporated; 14 pages, 3 figures; to appear in SIAM J. Discrete Math",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Tur\\'an number of an r-uniform hypergraph H is the maximum number of edges in any r-graph on n vertices which does not contain H as a subgraph. Let P_l^(r) denote the family of r-uniform loose paths on l edges, F(k,l) denote the family of hypergraphs consisting of k disjoint paths from P_l^(r), and P'_l^(r) denote an r-uniform linear path on l edges. We determine precisely ex_r(n;F(k,l)) and ex_r(n;k*P'_l^(r)), as well as the Tur\\'an numbers for forests of paths of differing lengths (whether these paths are loose or linear) when n is appropriately large dependent on k,l,r, for r>=3. Our results build on recent results of F\\\"uredi, Jiang, and Seiver who determined the extremal numbers for individual paths, and provide more hypergraphs whose Turan numbers are exactly determined.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-24T18:38:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C65",
      "05C35"
    ],
    "keywords": [
      "turán numbers",
      "turan number",
      "r-uniform loose paths",
      "r-uniform linear path",
      "appropriately large dependent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5022B"
    }
  }
}