didericis 3d1b1eb4a3 dual_decomposition: verify strengthened conjecture on 6 Holton-McKay duals ...

- New experiment experiments/check_conj_on_holton_mckay.py parses
  McKay's planar_code file of the 6 non-Hamiltonian 38-vertex cubic
  plane graphs (Holton-McKay) and tests both clauses (1)-(3) and (1)-(4)
  of the face-monochromatic-pair conjecture on each. Result: 17,280
  candidate colourings, all 17,280 satisfy both conjectures.
- Add a "Targeted check on the Holton-McKay duals" paragraph to
  Remark 4.4 with a per-graph table.
- Fix a latent bug in check_conj_3_8_scaled.py: b was hardcoded to
  cyc_b, leaving b == a when phi(e_1) == cyc_b (and consequently c
  ambiguous). Now correctly computes b = whichever of cyc_a/cyc_b is
  not a, raising if neither matches. The bug never crashed n <= 20
  because any() short-circuited on correctly-built witnesses; the
  Holton-McKay reductions hit it on the first witness, surfacing it.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

2026-05-24 14:45:56 -04:00

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