didericis
a22ca4b888
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>
25 lines
1.8 KiB
TeX
25 lines
1.8 KiB
TeX
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\citation{bauerfeld-medial-tire}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A full medial tire graph (left) and its walk-depth labelling and cut (right), from Example\nonbreakingspace 2.3\hbox {}. Black vertices are the annular medial vertices of the cycle $A(T)$; blue vertices are up-tooth apexes, red vertices are down-tooth apexes, and the larger red vertex is the shared apex of the bite on annular edges $0$ and $4$. On the right, each tooth carries its walk depth, and the two red slits mark the cuts: \emph {cut\nonbreakingspace 1} duplicates $a_5$ as the root-face traversal closes, and \emph {cut\nonbreakingspace 2} duplicates $a_1$ as the bite's inner-gap face closes. After the cuts the only bounded faces are the eight teeth.}}{3}{}\protected@file@percent }
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