{
  "abstract": "A graph $G$ is degree-truncated DP-$k$-colourable (respectively, degree-truncated $k$-choosable) if it is DP-$f$-colourable (respectively, $f$-choosable), where $f(v)=\\min\\{k,d_G(v)\\}$ for every vertex $v$. Hutchinson proved that every $2$-connected maximal outerplanar graph other than the triangle is degree-truncated $5$-choosable. Lo, Wang, Zhou and Zhu strengthened this result by proving that every $2$-connected $K_{2,4}$-minor-free graph other than cycles and complete graphs is degree-truncated DP-$5$-colourable. Outerplanar graphs are precisely the $\\{K_4,K_{2,3}\\}$-minor-free graphs. We study how the truncation threshold grows when $K_{2,3}$ is replaced by $K_{2,t}$, while $K_4$-minor remains excluded. A bound independent of $t$ is impossible, as shown by the family $\\{K_{2,n}| n\\ge 2\\}$. Let $\\mathcal S_t$ be the class of $2$-connected $\\{K_4,K_{2,t}\\}$-minor-free graphs other than cycles. Writing $χ^{\\text{\\sout{d}}}_{\\mathrm{DP}}(\\mathcal S_t)$ for the least truncation threshold valid throughout this class, we prove that, for every integer $t\\ge3$, \\[ \\left\\lfloor2\\sqrt{2t}\\right\\rfloor \\le χ^{\\text{\\sout{d}}}_{\\mathrm{DP}}(\\mathcal S_t) \\le \\left\\lceil4\\sqrt{2t}\\right\\rceil. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36586",
  "author_total": 1,
  "authors": [
    {
      "name": "Huan Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r1r62bw3atsd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36586",
  "fulltext_url": null,
  "id": "3r1r62bw3atsd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36586",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7224112862",
  "pdf_url": "https://arxiv.org/pdf/2610.36586",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r1r62bw3atsd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36586",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36586"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Degree-truncated DP-colouring of $\\{K_4,K_{2,t}\\}$-minor-free graphs",
  "title_text": "Degree-truncated DP-colouring of {K_4,K_2,t}-minor-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/3r1r62bw3atsd",
  "venue": "arXiv",
  "versions": []
}