{
  "id": "1401.4851",
  "version": "v1",
  "published": "2014-01-20T10:25:07.000Z",
  "updated": "2014-01-20T10:25:07.000Z",
  "title": "A characterization of hypergraphs that achieve equality in the Chvátal-McDiarmid Theorem",
  "authors": [
    "Michael A. Henning",
    "Christian Löwenstein"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For $k \\ge 2$, let $H$ be a $k$-uniform hypergraph on $n$ vertices and $m$ edges. The transversal number $\\tau(H)$ of $H$ is the minimum number of vertices that intersect every edge. Chv\\'{a}tal and McDiarmid [Combinatorica 12 (1992), 19--26] proved that $\\tau(H)\\le ( n + \\left\\lfloor \\frac k2 \\right\\rfloor m )/ ( \\left\\lfloor \\frac{3k}2 \\right\\rfloor )$. When $k = 3$, the connected hypergraphs that achieve equality in the Chv\\'{a}tal-McDiarmid Theorem were characterized by Henning and Yeo [J. Graph Theory 59 (2008), 326--348]. In this paper, we characterize the connected hypergraphs that achieve equality in the Chv\\'{a}tal-McDiarmid Theorem for $k = 2$ and for all $k \\ge 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-20T10:25:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C65"
    ],
    "keywords": [
      "achieve equality",
      "chvátal-mcdiarmid theorem",
      "characterization",
      "connected hypergraphs",
      "graph theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.4851H"
    }
  }
}