{
  "id": "2305.05868",
  "version": "v1",
  "published": "2023-05-10T03:21:11.000Z",
  "updated": "2023-05-10T03:21:11.000Z",
  "title": "Hadwiger's Conjecture for some graphs with independence number two",
  "authors": [
    "Tong Li",
    "Guiying Yan",
    "Qiang Zhou"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor, $\\chi(G)$ the chromatic number of $G$ respectively. In 1943, Hadwiger conjectured that $h(G) \\geq \\chi(G)$ for any graph $G$. In this paper, we will prove Hadwiger's Conjecture holds for $H$-free graphs with independence number two, where $H$ is any one of 4 given graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T03:21:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "independence number",
      "hadwigers conjecture holds",
      "free graphs",
      "chromatic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}