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math-research/papers/dual_decomposition_minimal_counterexamples/paper.log
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didericis 03dcd7c2fa dual_decomposition: swap algorithm trace to n=14 + final-graph conjecture 
- Replace the dodecahedron trace at the end of section 3 with the n=14
  triangulation found by search_kempe_property.py: its H_1 admits a
  proper 3-edge-colouring satisfying both chord-apex and Kempe-cycle
  conditions (Lemmas 2.6, 2.7).
- experiments/draw_iterated_reduction_n14.py: rebuilds fig_alg_step{0,1,2}
  with Tutte barycentric layouts (outer face chosen to keep v_n in the
  interior); also runs the algorithm to completion, checking chord-apex +
  Kempe at each step (step 1 satisfies all; step 2 fails chord-apex;
  step 3 terminates).
- Add Conjecture 3.4: G is a minimal counterexample iff no proper
  3-edge-colouring of the final reduced graph H_{t*} has all (spike_t,
  merged_t) pairs in distinct colours.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
2026-05-23 13:20:32 -04:00

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