{
  "id": "2102.13458",
  "version": "v1",
  "published": "2021-02-26T13:32:23.000Z",
  "updated": "2021-02-26T13:32:23.000Z",
  "title": "Chromatic bounds for the subclasses of $pK_2$-free graphs",
  "authors": [
    "Athmakoori Prashant",
    "S. Francis Raj",
    "M. Gokulnath"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the chromatic number for graphs with forbidden induced subgraphs. We improve the existing $\\chi$-binding functions for some subclasses of $2K_2$-free graphs, namely $\\{2K_2, H\\}$-free graphs where $H\\in \\{K_5-e, K_2+P_4, K_1 + C_4\\}$. In addition, for $p\\geq3$, we find the polynomial $\\chi$-binding functions $\\{pK_2, H\\}$-free graphs where $H\\in \\{gem, diamond, HVN, K_5-e, K_2+P_4, butterfly, dart, gem^+, C_4, K_1 + C_4, \\overline{P_5}\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-26T13:32:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C75"
    ],
    "keywords": [
      "free graphs",
      "chromatic bounds",
      "subclasses",
      "binding functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}