New experiments/run_medial_tire_cut_experiment.py: generates a random
maximal planar graph (stacked seed + random diagonal flips), builds the
medial graph, takes the tire decomposition at a random vertex level
source, walk-depth labels and cuts each full medial tire graph chained
down the tire tree, and assembles one final cut graph of M(G) with a
global label map (data only; graphics go in a separate script).
Fix label_and_cut: the root face is None, which collided with the
next(..., None) sentinel, leaving teeth unlabelled when the entry up
tooth lay inside a bite gap; use a distinct sentinel so the ascent to
the root face runs.
Add a "Chaining across the tire tree" section to the paper, clarifying
that the candidate parent down teeth are the boundary (singleton) down
teeth only -- bite teeth are interior to the parent and shared with no
child, so a lower-walk bite is skipped.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis
a22ca4b888