- 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>
didericis
1305006b50