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didericis b2eb7ef3cb dual_decomposition: scaffold paper + fill in minimal-counterexample step 
New paper "Dual Decomposition of Minimal Counterexamples" outlining a six-step
cut-and-recombine attack on the 4CT via the dual cubic graph: minimal
counterexample -> dualise -> minimum (cyclic) edge cut -> cap to cubic ->
3-edge-colour the pieces -> reconnect. Strategy section flags steps 1-5 as
standard machinery and step 6 (recombination) as the crux.

Step 1 written in full: reduction to triangulations, definition of the minimal
counterexample, minimum-degree >= 5 (degree <=3 and degree-4 Kempe cases), and
no separating triangle => 4-connected. 5-connectivity stated as Birkhoff's
separating-4-cycle reduction (attributed, not re-derived).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-05-22 17:56:24 -04:00

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