{
  "id": "1511.04356",
  "version": "v1",
  "published": "2015-11-13T16:49:57.000Z",
  "updated": "2015-11-13T16:49:57.000Z",
  "title": "A refinement of theorems on vertex-disjoint chorded cycles",
  "authors": [
    "Theodore Molla",
    "Michael Santana",
    "Elyse Yeager"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1963, Corr\\'adi and Hajnal settled a conjecture of Erd\\H{o}s by proving that, for all $k \\geq 1$, any graph $G$ with $|G| \\geq 3k$ and minimum degree at least $2k$ contains $k$ vertex-disjoint cycles. In 2008, Finkel proved that for all $k \\geq 1$, any graph $G$ with $|G| \\geq 4k$ and minimum degree at least $3k$ contains $k$ vertex-disjoint chorded cycles. Finkel's result was strengthened by Chiba, Fujita, Gao, and Li in 2010, who showed, among other results, that for all $k \\geq 1$, any graph $G$ with $|G| \\geq 4k$ and minimum Ore-degree at least $6k-1$ contains $k$ vertex-disjoint cycles. We refine this result, characterizing the graphs $G$ with $|G| \\geq 4k$ and minimum Ore-degree at least $6k-2$ that do not have $k$ disjoint chorded cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-13T16:49:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C38",
      "05C75"
    ],
    "keywords": [
      "vertex-disjoint chorded cycles",
      "minimum ore-degree",
      "refinement",
      "vertex-disjoint cycles",
      "minimum degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151104356M"
    }
  }
}