didericis 1305006b50 face_monochromatic_pairs: 28-vertex C28 fullerene is the smallest counterexample to Conj 5.5 (face-length ≥ 5 form) ...

- Conjecture 5.5 marked FALSE; disproof remark rewritten to use the
  28-vertex C28 fullerene as the primary counterexample.
- Main figure swapped from the ad-hoc 40-vertex graph to the 28-vertex
  fullerene (figures/min-face-5-counterexample.png). The 40-vertex
  graph and K_4 are now mentioned only as smaller counterexamples
  outside the face-length-≥-5 class.
- Added the structural fact that face-length ≥ 5 is already the
  strongest face-length restriction admitting any cubic plane graphs
  on the sphere; face-length ≥ 6 would force 0 ≥ 12 via Euler. So no
  further face-length strengthening can save the conjecture.

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

2026-05-25 03:44:41 -04:00

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