{
  "abstract": "Let $F$ be a connected color-critical graph with $χ(F)=r+1\\ge4$, let $S_{n,Δ}^{(r)}=(n-Δ)K_1\\vee T(Δ,r-1)$. We determine the graph of maximum adjacency spectral radius among all $n$-vertex $F$-free graphs with prescribed maximum degree $Δ$. There is a constant $s_F\\in[0,1)$ such that, for all sufficiently large $n$, $\\left\\lceil\\frac{(r-1)n}{r}\\right\\rceil\\le Δ\\le n-Θ(n^{s_F})$ implies that every $n$-vertex $F$-free graph $G$ with $Δ(G)=Δ$ satisfies $ρ(G)\\le ρ\\bigl(S_{n,Δ}^{(r)}\\bigr)$, with equality if and only if $G\\cong S_{n,Δ}^{(r)}$. This is the spectral counterpart of the edge theorem of [European J. Combin. 106 (2022), 103576.] and extends the clique result in [arXiv:2608.26634, 2026.]. This result also provides a benchmark for unbalanced spectral Turán problems arising from other extremal parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01114",
  "author_total": 1,
  "authors": [
    {
      "name": "Chang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9czkzb9z9xnc5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01114",
  "fulltext_url": null,
  "id": "9czkzb9z9xnc5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01114",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7206170592",
  "pdf_url": "https://arxiv.org/pdf/2609.01114",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9czkzb9z9xnc5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01114",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01114"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Unbalanced spectral Turán problem for color-critical graphs with prescribed large maximum degree",
  "title_text": "Unbalanced spectral Turán problem for color-critical graphs with prescribed large maximum degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/9czkzb9z9xnc5",
  "venue": "arXiv",
  "versions": []
}