{
  "id": "1701.06451",
  "version": "v1",
  "published": "2017-01-23T15:26:20.000Z",
  "updated": "2017-01-23T15:26:20.000Z",
  "title": "A Stability Theorem for Matchings in Tripartite 3-Graphs",
  "authors": [
    "Penny Haxell",
    "Lothar Narins"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "It follows from known results that every regular tripartite hypergraph of positive degree, with $n$ vertices in each class, has matching number at least $n/2$. This bound is best possible, and the extremal configuration is unique. Here we prove a stability version of this statement, establishing that every regular tripartite hypergraph with matching number at most $(1 + \\varepsilon)n/2$ is close in structure to the extremal configuration, where \"closeness\" is measured by an explicit function of $\\varepsilon$. We also answer a question of Aharoni, Kotlar and Ziv about matchings in hypergraphs with a more general degree condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-23T15:26:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stability theorem",
      "regular tripartite hypergraph",
      "extremal configuration",
      "matching number",
      "general degree condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}