{
  "id": "1107.4947",
  "version": "v3",
  "published": "2011-07-25T13:27:39.000Z",
  "updated": "2011-08-08T00:51:57.000Z",
  "title": "On a Greedy 2-Matching Algorithm and Hamilton Cycles in Random Graphs with Minimum Degree at Least Three",
  "authors": [
    "Alan Frieze"
  ],
  "comment": "Companion paper to \"On a sparse random graph with minimum degree {three}: Likely Posa's sets are large\"",
  "categories": [
    "math.CO"
  ],
  "abstract": "We describe and analyse a simple greedy algorithm \\2G\\ that finds a good 2-matching $M$ in the random graph $G=G_{n,cn}^{\\d\\geq 3}$ when $c\\geq 15$. A 2-matching is a spanning subgraph of maximum degree two and $G$ is drawn uniformly from graphs with vertex set $[n]$, $cn$ edges and minimum degree at least three. By good we mean that $M$ has $O(\\log n)$ components. We then use this 2-matching to build a Hamilton cycle in $O(n^{1.5+o(1)})$ time \\whp.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-08-08T00:51:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimum degree",
      "hamilton cycle",
      "random graph",
      "simple greedy algorithm",
      "maximum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.4947F"
    }
  }
}