{
  "id": "1406.7453",
  "version": "v2",
  "published": "2014-06-29T01:33:32.000Z",
  "updated": "2015-08-19T20:06:37.000Z",
  "title": "The (2k-1)-connected multigraphs with at most k-1 disjoint cycles",
  "authors": [
    "H. A. Kierstead",
    "A. V. Kostochka",
    "E. C. Yeager"
  ],
  "comment": "7 pages, 2 figures. To appear in Combinatorica",
  "doi": "10.1007/s00493-015-3291-8",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1963, Corr\\'adi and Hajnal proved that for all $k \\ge 1$ and $n \\ge 3k$, every (simple) graph on n vertices with minimum degree at least 2k contains k disjoint cycles. The same year, Dirac described the 3-connected multigraphs not containing two disjoint cycles and asked the more general question: Which (2k-1)-connected multigraphs do not contain k disjoint cycles? Recently, the authors characterized the simple graphs G with minimum degree $\\delta(G) \\ge 2k-1$ that do not contain k disjoint cycles. We use this result to answer Dirac's question in full.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-29T01:33:32.000Z",
      "comment": "7 pages, 2 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-08-19T20:06:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C35",
      "05C40"
    ],
    "keywords": [
      "disjoint cycles",
      "multigraphs",
      "minimum degree",
      "answer diracs question",
      "simple graphs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7453K"
    }
  }
}