{
  "id": "1906.01433",
  "version": "v1",
  "published": "2019-05-31T20:53:13.000Z",
  "updated": "2019-05-31T20:53:13.000Z",
  "title": "Hamilton cycles in random graphs with minimum degree at least 3: an improved analysis",
  "authors": [
    "Michael Anastos",
    "Alan Frieze"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1107.4947",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we consider the existence of Hamilton cycles in the random graph $G=G_{n,m}^{\\delta\\geq 3}$. This a random graph chosen uniformly from the set of graphs with vertex set $[n]$, $m$ edges and minimum degree at least 3. Our ultimate goal is to prove that if $m=cn$ and $c>3/2$ is constant then $G$ is Hamiltonian w.h.p. In an earlier paper the second author showed that $c\\geq 10$ is sufficient for this and in this paper we reduce the lower bound to $c>2.662...$. This new lower bound is the same lower bound found in Frieze and Pittel \\cite{FP} for the expansion of so-called Pos\\'a sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-31T20:53:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton cycles",
      "minimum degree",
      "lower bound",
      "random graph chosen",
      "posa sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}