didericis
192ad33bd2
- Update def:edge-names to distinguish side-0 ({A_i, v_n}) and side-1
({A_{i+2}, v_n}); merged and spike unchanged.
- Add a paragraph defining the {a,b}-Kempe cycle in a 3-edge-coloured cubic
graph.
- Add lem:kempe-spike: in any proper 3-edge-colouring of the reduced dual,
the {c, c_0}-Kempe cycle through the spike contains side-0 and merged
(symmetrically for side-1 with c_1).
- Proof by Kempe swap: a hypothetical alternative cycle K containing merged
but not spike would, after swapping c <-> c_0 on K, give a proper
3-edge-colouring under which spike and merged disagree --- contradicting
lem:chord-apex.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
math-research
Personal mathematics research repository by Eric Bauerfeld. Papers are written in AMS-LaTeX using the amsart document class.
Papers
kempe_style_search_for_smaller_contradiction
Humans Suffice: A Novel Proof of the Four Color Theorem
An in-progress proof of the Four Color Theorem via a minimal counterexample argument. The paper builds on Kempe's 1879 strategy — establishing valid cases for vertices of degree ≤ 4, then extending the argument to the degree-5 case using properties of non-adjacent degree-5 vertices, merged subgraphs, and locked colorings.
plane_depth_labelling
Plane Depth Labelling
Early-stage paper. Title and author information set; content in progress.
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