{
  "id": "2006.03009",
  "version": "v1",
  "published": "2020-06-04T16:56:47.000Z",
  "updated": "2020-06-04T16:56:47.000Z",
  "title": "List-three-coloring $ P_t $-free graphs with no induced 1-subdivision of $ K_{1,s} $",
  "authors": [
    "Maria Chudnovsky",
    "Sophie Spirkl",
    "Mingxian Zhong"
  ],
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Let $s$ and $t$ be positive integers. We use $P_t$ to denote the path with $t$ vertices and $K_{1,s}$ to denote the complete bipartite graph with parts of size $1$ and $s$ respectively. The one-subdivision of $K_{1,s}$ is obtained by replacing every edge $\\{u,v\\}$ of $K_{1,s}$ by two edges $\\{u,w\\}$ and $\\{v,w\\}$ with a new vertex $w$. In this paper, we give a polynomial-time algorithm for the list-three-coloring problem restricted to the class of $P_t$-free graph with no induced 1-subdivision of $K_{1,s}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-04T16:56:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free graph",
      "complete bipartite graph",
      "polynomial-time algorithm",
      "positive integers",
      "one-subdivision"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}