{
  "id": "2006.02015",
  "version": "v1",
  "published": "2020-06-03T02:36:22.000Z",
  "updated": "2020-06-03T02:36:22.000Z",
  "title": "Coloring $(P_5, \\text{gem})$-free graphs with $Δ-1$ colors",
  "authors": [
    "Daniel W. Cranston",
    "Hudson Lafayette",
    "Landon Rabern"
  ],
  "comment": "8 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Borodin-Kostochka Conjecture states that for a graph $G$, if $\\Delta(G) \\geq 9$ and $\\omega(G) \\leq \\Delta(G)-1$, then $\\chi(G)\\leq\\Delta(G) -1$. We prove the Borodin-Kostochka Conjecture for $(P_5, \\text{gem})$-free graphs, i.e., graphs with no induced $P_5$ and no induced $K_1\\vee P_4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-03T02:36:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "free graphs",
      "borodin-kostochka conjecture states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}