{
  "id": "2406.06035",
  "version": "v1",
  "published": "2024-06-10T05:57:48.000Z",
  "updated": "2024-06-10T05:57:48.000Z",
  "title": "Truncated-degree-choosability of planar graphs",
  "authors": [
    "Yiting Jiang",
    "Huijuan Xu",
    "Xinbo Xu",
    "Xuding Zhu"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Assume $G$ is a graph and $k$ is a positive integer. Let $f:V(G)\\to N$ be defined as $f(v)=\\min\\{k,d_G(v)\\}$. If $G$ is $f$-choosable, then we say $G$ is $k$-truncated-degree-choosable. It was proved in [Zhou,Zhu,Zhu, Arc-weighted acyclic orientations and variations of degeneracy of graphs, arXiv:2308.15853] that there is a 3-connected non-complete planar graph that is not 7-truncated-degree-choosable, and every 3-connected non-complete planar graph is 16-truncated-degree-choosable. This paper improves the bounds, and proves that there is a 3-connected non-complete planar graph that is not 8-truncated-degree-choosable and every non-complete 3-connected planar graph is 12-truncated-degree-choosable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-10T05:57:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-complete planar graph",
      "truncated-degree-choosability",
      "arc-weighted acyclic orientations",
      "positive integer",
      "variations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}