{
  "id": "1211.3263",
  "version": "v1",
  "published": "2012-11-14T10:28:43.000Z",
  "updated": "2012-11-14T10:28:43.000Z",
  "title": "Optimal packings of Hamilton cycles in graphs of high minimum degree",
  "authors": [
    "Daniela Kühn",
    "John Lapinskas",
    "Deryk Osthus"
  ],
  "comment": "Accepted to Combinatorics, Probability and Computing",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the number of edge-disjoint Hamilton cycles one can guarantee in a sufficiently large graph G on n vertices with minimum degree d = (1/2+a)n. For any constant a > 0, we give an optimal answer in the following sense: let reg_even(n,d) denote the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree d. Then the number of edge-disjoint Hamilton cycles we find equals reg_even(n,d)/2. The value of reg_even(n,d) is known for infinitely many values of n and d. We also extend our results to graphs G of minimum degree d >= n/2, unless G is close to the extremal constructions for Dirac's theorem. Our proof relies on a recent and very general result of K\\\"uhn and Osthus on Hamilton decomposition of robustly expanding regular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-14T10:28:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C45",
      "05C70"
    ],
    "keywords": [
      "high minimum degree",
      "optimal packings",
      "edge-disjoint hamilton cycles",
      "largest even-regular spanning subgraph",
      "robustly expanding regular graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3263K"
    }
  }
}