didericis/math-research
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Add medial tire cut experiment and chaining section

Browse Source 
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>
This commit is contained in:
didericis
2026-06-14 23:46:49 -04:00
parent b4ddc7da8b
commit a22ca4b888
6 changed files with 388 additions and 33 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/medial_tire_cuts/paper.aux
+10 -6
View File
@@ -6,15 +6,19 @@
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Cutting a full medial tire graph}}{1}{}\protected@file@percent }
\newlabel{def:walk-depth-cut}{{2.1}{1}}
\citation{bauerfeld-medial-tire}
\citation{bauerfeld-medial-tire}
\newlabel{rem:closing-tooth}{{2.2}{2}}
\newlabel{ex:worked-cut}{{2.3}{2}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Chaining across the tire tree}}{2}{}\protected@file@percent }
\citation{bauerfeld-medial-tire}
\bibcite{bauerfeld-medial-tire}{1}
\@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 }
\newlabel{fig:worked-cut}{{1}{3}}
\newlabel{rem:chaining-candidates}{{3.1}{3}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\newlabel{rem:closing-tooth}{{2.2}{2}}
\newlabel{ex:worked-cut}{{2.3}{2}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{2}{}\protected@file@percent }
\@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 }
\newlabel{fig:worked-cut}{{1}{3}}
\gdef \@abspage@last{3}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{4}{}\protected@file@percent }
\gdef \@abspage@last{4}