Graph Recoloring Diameter Bounds for Treewidth-2 Graphs — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The search domain query returned heterogeneous arXiv abstracts with no direct mathematical core on information complexity or convex optimization lower bounds; the closest structural result is the graph recoloring theorem for treewidth-2 graphs. | MATH: Jerrum's theorem: any $(d+2)$-coloring of a $d$-degenerate graph transforms via adjacent colorings (differing on one vertex). For treewidth 2, the recoloring diameter is polynomial; Bonamy et al. bound shortest transformation length. No explicit constants, ratios, or equations beyond the $(d+2)$ bound. | CONNECTION: Treewidth 2 graphs are subgraphs of series-parallel graphs, which have a natural decomposition tree — a binary tree structure. The recoloring adjacency graph on colorings forms a lattice-like structure, but no golden ratio, base-60, or crystallographic symmetry appears. The $(d+2)$ bound is tight in general, but for treewidth 2 the structure is more constrained, echoing the rigidity of planar graphs (Euler characteri Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208824314
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