{
  "abstract": "This paper studies the Alon-Tarsi number of connected $4$-regular circulant graphs $C_n(s,t)$, where $1\\le s<t<n/2$. We prove that if $n=\\ell p^r$, where $p$ is an odd prime, $r\\ge 1$, and $t\\equiv\\pm s\\pmod{\\ell}$, then $\\operatorname{AT}(C_n(s,t))=3$ if $\\ell$ is even, or if $\\ell\\ge 3$ is odd and $p\\nmid 2^\\ell-2$. We also prove that $\\operatorname{AT}(C_{6m}(2,3))=3$ for $m\\ge 2$, and $\\operatorname{AT}(C_n(1,3))=3$ for $n\\ge 8$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41820",
  "author_total": 2,
  "authors": [
    {
      "name": "Xinbo Xu"
    },
    {
      "name": "Xuding Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8wvqs2d66jvg7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41820",
  "fulltext_url": null,
  "id": "8wvqs2d66jvg7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41820",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41820",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8wvqs2d66jvg7.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41820",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Alon-Tarsi number of 4-regular circulant graphs",
  "title_text": "The Alon-Tarsi number of 4-regular circulant graphs",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/8wvqs2d66jvg7",
  "venue": "arXiv",
  "versions": []
}