{
  "abstract": "FINDING: The search results are dominated by unrelated physics/CS papers; the only mathematically substantive item is a graph recoloring theorem for treewidth-2 graphs. | MATH: Jerrum's theorem: any $(d+2)$-coloring of a $d$-degenerate graph transforms via adjacent colorings; treewidth-2 graphs are $K_4$-minor-free, and their recoloring diameter is polynomial (Bonamy et al. result on shortest transformation length). | CONNECTION: Treewidth-2 graphs are exactly partial 2-trees — their structure relates to series-parallel decompositions, which are built from series and parallel compositions, echoing the golden-ratio-free but *binary tree* recursion. No direct 0.618/1.618 ratio appears. However, the degeneracy $d$ and coloring bound $d+2$ mirror the chromatic polynomial's root structure; for $d=2$, the bound is 4 colors, and the 4-color theorem's planar case is a special limit. | DEPTH: 3 — This is a combinatorial graph theory result with algorithmic implications (recoloring paths), but i\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewsmnayykgd2s.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587152",
  "fulltext_url": null,
  "id": "ewsmnayykgd2s",
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  "landing_url": "https://zenodo.org/records/23587152",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewsmnayykgd2s.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:51Z",
      "native_id": "23587152",
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      "url": "https://zenodo.org/records/23587152"
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  "subjects": [],
  "title": "Recoloring Treewidth-2 Graphs: Polynomial Diameter via Degeneracy — E8 Intelligence Research",
  "title_text": "Recoloring Treewidth-2 Graphs: Polynomial Diameter via Degeneracy — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:51Z",
  "url": "https://research.draconitic.com/paper/ewsmnayykgd2s",
  "venue": "Zenodo",
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}