{
  "abstract": "We prove that every $(2K_2,K_4)$-free graph is recolorable. Equivalently, for every such graph $G$ and every $\\ell\\geq χ(G)+1$, the reconfiguration graph of proper $\\ell$-colorings of $G$, in which two colorings are adjacent if they differ on exactly one vertex, is connected. This resolves the final remaining open case in the classification of recolorable $(F_1,F_2)$-free graphs when $F_1$ and $F_2$ have at most four vertices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28893",
  "author_total": 2,
  "authors": [
    {
      "name": "Henry Echeverría"
    },
    {
      "name": "Owen Henderschedt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahksts06h82qj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28893",
  "fulltext_url": null,
  "id": "ahksts06h82qj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28893",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214283877",
  "pdf_url": "https://arxiv.org/pdf/2609.28893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahksts06h82qj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Yes, $(2K_2, K_4)$-free graphs are recolorable",
  "title_text": "Yes, (2K_2, K_4)-free graphs are recolorable",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/ahksts06h82qj",
  "venue": "arXiv",
  "versions": []
}