{
  "id": "1911.08686",
  "version": "v1",
  "published": "2019-11-20T03:41:02.000Z",
  "updated": "2019-11-20T03:41:02.000Z",
  "title": "On Degree Sum Conditions and Vertex-Disjoint Chorded Cycles",
  "authors": [
    "Bradley Elliott",
    "Ronald Gould",
    "Kazuhide Hirohata"
  ],
  "comment": "16 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we consider a general degree sum condition sufficient to imply the existence of $k$ vertex-disjoint chorded cycles in a graph $G$. Let $\\sigma_t(G)$ be the minimum degree sum of $t$ independent vertices of $G$. We prove that if $G$ is a graph of sufficiently large order and $\\sigma_t(G)\\geq 3kt-t+1$ with $k\\geq 1$, then $G$ contains $k$ vertex-disjoint chorded cycles. We also show that the degree sum condition on $\\sigma_t(G)$ is sharp. To do this, we also investigate graphs without chorded cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-20T03:41:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vertex-disjoint chorded cycles",
      "general degree sum condition sufficient",
      "minimum degree sum",
      "independent vertices",
      "sufficiently large order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}