{
  "id": "1505.08127",
  "version": "v1",
  "published": "2015-05-29T18:02:08.000Z",
  "updated": "2015-05-29T18:02:08.000Z",
  "title": "Extremal results for Berge-hypergraphs",
  "authors": [
    "Dániel Gerbner",
    "Cory Palmer"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph and $\\mathcal{H}$ be a hypergraph both on the same vertex set. We say that a hypergraph $\\mathcal{H}$ is a \\emph{Berge}-$G$ if there is a bijection $f : E(G) \\rightarrow E(\\mathcal{H})$ such that for $e \\in E(G)$ we have $e \\subset f(e)$. This generalizes the established definitions of \"Berge path\" and \"Berge cycle\" to general graphs. For a fixed graph $G$ we examine the maximum possible size (i.e.\\ the sum of the cardinality of each edge) of a hypergraph with no Berge-$G$ as a subhypergraph. In the present paper we prove general bounds for this maximum when $G$ is an arbitrary graph. We also consider the specific case when $G$ is a complete bipartite graph and prove an analogue of the K\\H ov\\'ari-S\\'os-Tur\\'an theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-29T18:02:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extremal results",
      "berge-hypergraphs",
      "complete bipartite graph",
      "vertex set",
      "specific case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}