{
  "id": "1303.5139",
  "version": "v2",
  "published": "2013-03-21T01:48:11.000Z",
  "updated": "2014-02-04T16:27:05.000Z",
  "title": "The first k-regular subgraph is large",
  "authors": [
    "Pu Gao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for sufficiently large k, there exist $0\\le\\sigma_k\\le\\eps_k\\to 0$ as $k\\to\\infty$, such that asymptotically almost surely the first k-regular subgraph appeared in the random graph process where one edge is added at a time has size between $(1-\\eps_k)|\\K_k|$ and $(1-\\sigma_k)|\\K_k|$, where $\\K_k$ denotes the $k$-core of the graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-04T16:27:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random graph process",
      "first k-regular subgraph",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5139G"
    }
  }
}