{
  "id": "2308.05442",
  "version": "v1",
  "published": "2023-08-10T08:58:12.000Z",
  "updated": "2023-08-10T08:58:12.000Z",
  "title": "Optimal chromatic bound for ($P_3\\cup P_2$, house)-free graphs",
  "authors": [
    "Rui Li",
    "Di Wu",
    "Jinfeng Li"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2307.11946",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ and $H$ be two vertex disjoint graphs. The {\\em union} $G\\cup H$ is the graph with $V(G\\cup H)=V(G)\\cup V(H)$ and $E(G\\cup H)=E(G)\\cup E(H)$. We use $P_k$ to denote a {\\em path} on $k$ vertices, use {\\em house} to denote the complement of $P_5$. In this paper, we show that $\\chi(G)\\le2\\omega(G)$ if $G$ is ($P_3\\cup P_2$, house)-free. Moreover, this bound is optimal when $\\omega(G)\\ge2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-10T08:58:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal chromatic bound",
      "vertex disjoint graphs",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}