Adds tree_structure_sweep.py running the parent-child detection on
ALL 6-edge cuts found by greedy BFS-search on:
- 6 Holton-McKay non-Hamiltonian cubic plane graphs (HM #0-5).
- Dodecahedron (cubic dual of icosahedron, which is a min-degree-5
max planar graph).
Total 743 distinct 6-edge cuts × 2 sides each = 1486 tests.
Total cut tires examined: 11,477.
Tree-structure failures (cycles in parent relation): 0.
Per-graph cut counts:
HM #0: 128 cuts (all trees both sides)
HM #1: 127, HM #2: 122, HM #3: 123, HM #4: 101, HM #5: 97
Dodecahedron: 45 cuts (all trees both sides)
NOTE on the user's request: strictly "min-deg-5 with vertex-conn-6"
maximal planar graphs are incompatible (max planar avg deg < 6 ⇒
some vertex has degree ≤ 5 ⇒ vertex conn ≤ 5). Test coverage thus
includes:
- HM duals (21-vertex max planar, min-deg 4, vertex-conn 3): close
to the 4CT-relevant configurations.
- Icosahedron (12-vertex 5-regular, vertex-conn 5): min-deg 5
case.
Bug fix: previous cycle-detection logic in is_tree() always reported
a false-positive cycle (it added the current node to seen, then
trivially checked "cur in seen" after exit). Replaced with a clean
walk-up-from-each-node algorithm that detects actual cycles only.
Adds:
experiments/tree_structure_sweep.py
experiments/tree_structure_sweep_data.txt
Updates notes/cut_tire_tree_structure.tex with broader sweep table
and totals. Note grows to 4 pages.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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