Draw a medial tire cut from a random n=20 graph

Add experiments/draw_medial_tire_cut.py, the paper-graphics companion
that imports run_experiment and emits a TikZ panel (walk-depth labels +
cut slits) per recognised tread via to_tikz. Add the resulting figure
(Example 3.2, Figure 2): the single recognised tread T_2 of the medial
tire decomposition of a random maximal planar graph on 20 vertices
(seed 72), an 8-cycle piece with a bite, labelled and cut.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

papers/medial_tire_cuts/experiments/draw_medial_tire_cut.py

@@ -0,0 +1,63 @@
+"""Draw the walk-depth labelling and cut of a medial tire decomposition.
+
+Paper-graphics companion to ``run_medial_tire_cut_experiment.py``: it imports
+``run_experiment`` from there, runs the pipeline on a random maximal planar
+graph, and emits a TikZ ``tikzpicture`` (walk-depth labels + cut slits) for each
+recognised full medial tire graph of the decomposition, using ``to_tikz`` from
+``medial_tire_cut_labelling``.
+
+This script only renders; the experiment itself draws nothing.  Run with the
+repo venv (networkx): ``.venv/bin/python``.
+
+Example:
+    .venv/bin/python draw_medial_tire_cut.py -n 20 --seed 72 > panels.tex
+"""
+
+from __future__ import annotations
+
+import argparse
+import os
+import sys
+
+_HERE = os.path.dirname(os.path.abspath(__file__))
+sys.path.insert(0, _HERE)
+
+from run_medial_tire_cut_experiment import run_experiment  # noqa: E402
+from medial_tire_cut_labelling import to_tikz  # noqa: E402
+
+
+def tikz_panels(n: int, seed: int, scale: float = 1.6) -> tuple[dict, list[str]]:
+    """Run the experiment and return ``(result, panels)``, one TikZ panel per
+    recognised tread, each showing that tread's walk-depth labelling and cut."""
+    result = run_experiment(n=n, seed=seed)
+    panels = []
+    for d in sorted(result["results"]):
+        rec = result["results"][d]
+        panels.append(to_tikz(rec["g"], depth=rec["depth"], cuts=rec["cuts"],
+                              entry_edge=rec["entry_edge"], scale=scale))
+    return result, panels
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description=__doc__,
+                                     formatter_class=argparse.RawDescriptionHelpFormatter)
+    parser.add_argument("-n", type=int, default=20)
+    parser.add_argument("--seed", type=int, default=72)
+    parser.add_argument("--scale", type=float, default=1.6)
+    args = parser.parse_args()
+
+    result, panels = tikz_panels(args.n, args.seed, scale=args.scale)
+    treads = sorted(result["results"])
+    print(f"% medial tire cut: n={args.n} seed={args.seed} "
+          f"source={result['source']} recognised treads={treads}")
+    if not panels:
+        print("% (no recognised full medial tire graphs for this graph)")
+    for d, panel in zip(treads, panels):
+        g = result["results"][d]["g"]
+        print(f"% --- tread {d}: |A(T)|={g.n} word={g.tooth_word} "
+              f"bites={sorted(g.bites)} ---")
+        print(panel)
+
+
+if __name__ == "__main__":
+    main()

papers/medial_tire_cuts/paper.aux

@@ -11,14 +11,17 @@
 \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{ex:real-cut}{{3.2}{3}}
+\bibcite{bauerfeld-medial-tire}{1}
 \newlabel{tocindent-1}{0pt}
 \newlabel{tocindent0}{12.7778pt}
 \newlabel{tocindent1}{17.77782pt}
 \newlabel{tocindent2}{0pt}
 \newlabel{tocindent3}{0pt}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The recognised tread $T_2$ of the medial tire decomposition of a random maximal planar graph on $20$ vertices (Example\nonbreakingspace 3.2\hbox {}), with its walk-depth labelling and cut. Black vertices are the annular medial vertices of $A(T)$; blue vertices are up-tooth apexes and red vertices down-tooth apexes, the larger red vertex being the shared apex of the bite on annular edges $2$ and $5$. Each tooth carries its walk depth; the red slits are the two cuts.}}{4}{}\protected@file@percent }
+\newlabel{fig:real-cut}{{2}{4}}
 \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{4}{}\protected@file@percent }
 \gdef \@abspage@last{4}

papers/medial_tire_cuts/paper.log

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papers/medial_tire_cuts/paper.tex

@@ -309,6 +309,84 @@ graph, tire decomposition at a vertex level source, and chained walk-depth
 labelling and cut---is carried out by the experiment script
 \texttt{experiments/run\_medial\_tire\_cut\_experiment.py}.
 
+\begin{example}[A medial tire cut from a random graph]
+\label{ex:real-cut}
+Run on a random maximal planar graph on $20$ vertices (seed $72$, level
+source vertex $9$), the experiment yields a single recognised tread
+$T_2$, drawn in Figure~\ref{fig:real-cut} with the walk-depth labelling
+and cut emitted by the graphics companion
+\texttt{experiments/draw\_medial\_tire\_cut.py}.  Its annular cycle has
+length $8$, with up teeth on annular edges $0,3,4$, singleton down teeth
+on $1,6,7$, and a bite on the non-incident annular edges $2$ and $5$ (the
+central shared apex).  Entering at the up tooth on edge $0$ with walk
+depth $0$, the root face is labelled in order ($0,1,2$ then $3,4,5$) and
+\emph{cut~1} duplicates $a_0$ as it closes; the walk then descends through
+the bite into its inner-gap face, labelling the two teeth there ($6,7$),
+and \emph{cut~2} duplicates $a_3$ as that face closes.  The two cuts leave
+only the outer face and the eight teeth as $3$-faces.
+\end{example}
+
+\begin{figure}[h]
+\centering
+\begin{tikzpicture}[scale=1.6,
+    ann/.style={circle, fill=black, inner sep=1.0pt},
+    upv/.style={circle, draw=blue!70!black, fill=blue!12, inner sep=1.4pt},
+    downv/.style={circle, draw=red!70!black, fill=red!12, inner sep=1.4pt},
+    bitev/.style={circle, draw=red!70!black, fill=red!32, inner sep=1.7pt},
+    cyc/.style={black, line width=1.0pt},
+    tth/.style={black!55, line width=0.4pt},
+    lbl/.style={font=\scriptsize},
+    dlbl/.style={font=\scriptsize\bfseries, text=black},
+    cut/.style={red!80!black, line width=1.3pt},
+    cutlbl/.style={font=\tiny, text=red!75!black}]
+\draw[cyc] (0.000,1.000)--(0.707,0.707)--(1.000,0.000)--(0.707,-0.707)--(0.000,-1.000)--(-0.707,-0.707)--(-1.000,-0.000)--(-0.707,0.707)--cycle;
+\draw[tth] (0.559,1.349)--(0.000,1.000) (0.559,1.349)--(0.707,0.707);
+\draw[tth] (0.559,-1.349)--(0.707,-0.707) (0.559,-1.349)--(0.000,-1.000);
+\draw[tth] (-0.559,-1.349)--(0.000,-1.000) (-0.559,-1.349)--(-0.707,-0.707);
+\draw[tth] (0.554,0.230)--(0.707,0.707) (0.554,0.230)--(1.000,0.000);
+\draw[tth] (-0.554,0.230)--(-1.000,-0.000) (-0.554,0.230)--(-0.707,0.707);
+\draw[tth] (-0.230,0.554)--(-0.707,0.707) (-0.230,0.554)--(0.000,1.000);
+\draw[tth] (0.000,-0.318)--(1.000,0.000) (0.000,-0.318)--(0.707,-0.707);
+\draw[tth] (0.000,-0.318)--(-0.707,-0.707) (0.000,-0.318)--(-1.000,-0.000);
+\node[ann] at (0.000,1.000) {};
+\node[ann] at (0.707,0.707) {};
+\node[ann] at (1.000,0.000) {};
+\node[ann] at (0.707,-0.707) {};
+\node[ann] at (0.000,-1.000) {};
+\node[ann] at (-0.707,-0.707) {};
+\node[ann] at (-1.000,-0.000) {};
+\node[ann] at (-0.707,0.707) {};
+\node[upv] at (0.559,1.349) {};
+\node[upv] at (0.559,-1.349) {};
+\node[upv] at (-0.559,-1.349) {};
+\node[downv] at (0.554,0.230) {};
+\node[downv] at (-0.554,0.230) {};
+\node[downv] at (-0.230,0.554) {};
+\node[bitev] at (0.000,-0.318) {};
+\node[dlbl] at (0.456,1.101) {0};
+\node[dlbl] at (0.704,0.292) {1};
+\node[dlbl] at (0.427,-0.336) {2};
+\node[dlbl] at (0.456,-1.101) {7};
+\node[dlbl] at (-0.456,-1.101) {6};
+\node[dlbl] at (-0.427,-0.336) {3};
+\node[dlbl] at (-0.704,0.292) {4};
+\node[dlbl] at (-0.292,0.704) {5};
+\draw[cut] (0.000,0.840)--(0.000,1.160);
+\node[cutlbl] at (0.000,1.300) {cut 1};
+\draw[cut] (0.594,-0.594)--(0.820,-0.820);
+\node[cutlbl] at (0.919,-0.919) {cut 2};
+\node[lbl, text=blue!60!black] at (0.689,1.663) {entry};
+\end{tikzpicture}
+\caption{The recognised tread $T_2$ of the medial tire decomposition of a
+random maximal planar graph on $20$ vertices
+(Example~\ref{ex:real-cut}), with its walk-depth labelling and cut.  Black
+vertices are the annular medial vertices of $A(T)$; blue vertices are
+up-tooth apexes and red vertices down-tooth apexes, the larger red vertex
+being the shared apex of the bite on annular edges $2$ and $5$.  Each
+tooth carries its walk depth; the red slits are the two cuts.}
+\label{fig:real-cut}
+\end{figure}
+
 \begin{thebibliography}{9}
 
 \bibitem{bauerfeld-medial-tire}