Recoloring Treewidth-2 Graphs: Polynomial Diameter via Degeneracy — E8 Intelligence Research

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 K₄-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 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com