{
  "id": "2206.14309",
  "version": "v1",
  "published": "2022-06-28T22:35:25.000Z",
  "updated": "2022-06-28T22:35:25.000Z",
  "title": "Linear-sized minors with given edge density",
  "authors": [
    "Tung H. Nguyen"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "It is proved that for every $\\varepsilon>0$, there exists $c>0$ such that for every $t\\ge2$, every graph with chromatic number at least $t$ contains a minor with at least $ct$ vertices and at most an $\\varepsilon$ fraction of all possible edges missing. This is related to linear Hadwiger's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-28T22:35:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edge density",
      "linear-sized minors",
      "linear hadwigers conjecture",
      "chromatic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}