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math-research/papers/level_resolutions_of_maximal_planar_graphs/paper.out
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didericis db245eecea Prove outerplanarity and draft edge-flip resolution algorithm 
- Promote Prop 3.1 (outerplanarity of level subgraphs) to Theorem 3.1
  with a proof by contradiction via a BFS-path argument; drop the
  $n \leq 10$ caveat and the now-resolved open question.
- Add Section 5 "An edge-flip resolution algorithm": apex classification
  of $L_k$-edges, bridge lemma, cross-level flip pass, definition of
  tricky-everywhere odd cycles and facial depth (seeded from inner
  faces with $\geq 2$ outer-face edges), and the depth-guided flip
  procedure. Observation 5.5 records empirical termination at
  $n = 9, 10, 11$; Question 5.6 asks if it holds in general.
- Add experiments/depth_monovariant_check.py (sanity check over
  triangulation iso-classes, confirms the count-of-tricky-faces
  monovariant strictly decreases per flip on all 1400 tricky configs
  at $n \leq 11$), viz_cycling.py and debug_cycling.py, and
  cycling_visualization.png illustrating the depth-definition fix.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
2026-05-20 01:20:27 -04:00

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