{
  "abstract": "The $k$-reconfiguration graph $R_k(G)$ of the proper $k$-colorings of a graph $G$ is the graph whose vertices are the $k$-colorings of $G$, with an edge between two colorings if they differ on exactly one vertex. A graph $G$ is recolorable if $R_k(G)$ is connected for all $k \\ge χ(G) + 1$. In this paper, we study recolorability under blowups through frozen colorings, here blowup means replacing vertices with non-empty cliques. We characterize frozen colorings of a blowup of $G$ in terms of maximal independent sets of the base graph, and develop a lifting principle that transfers suitable frozen obstructions from an induced subgraph to a blowup of the ambient graph. This framework yields several consequences. In particular, we answer negatively a question of Belavadi, Cameron and Sintiari on recoloring via modular decomposition, and disprove their conjecture on blowups of prime graphs. We further determine exactly which cycles have all blowups recolorable: this holds for $C_n$ if and only if $n\\in\\{3,4,5,7\\}$. The frozen obstructions arising from the negative cases, together with the lifting principle, imply that if every blowup of a graph $G$ is recolorable, then every induced hole of $G$ has length $4$, $5$, or $7$. Finally, using linear programming duality, we show that every such graph $G$ is fractionally co-strongly perfect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27527",
  "author_total": 3,
  "authors": [
    {
      "name": "Tianyu Huang"
    },
    {
      "name": "Yulai Ma"
    },
    {
      "name": "Jiaqi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03wjs25da5y59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27527",
  "fulltext_url": null,
  "id": "03wjs25da5y59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27527",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223112670",
  "pdf_url": "https://arxiv.org/pdf/2610.27527",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03wjs25da5y59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27527",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27527"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Frozen colorings and recolorability of blowups",
  "title_text": "Frozen colorings and recolorability of blowups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/03wjs25da5y59",
  "venue": "arXiv",
  "versions": []
}