Draw the whole medial graph with all tire cuts

Add a --whole mode to draw_medial_tire_cut.py that renders the entire
medial graph M(G) (the assembled cut graph), on a Kamada-Kawai layout,
with the recognised tires highlighted (black annular vertices, blue/red
teeth carrying walk depths, larger red bite apex) and the rest of M(G)
in grey. Add the resulting figure (Figure 3) and a describing paragraph
to the paper for the n=20 seed-72 example, via an \input-ed .tikz file.

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

papers/medial_tire_cuts/paper.tex

@@ -387,6 +387,31 @@ tooth carries its walk depth; the red slits are the two cuts.}
 \label{fig:real-cut}
 \end{figure}
 
+The same data sit inside the whole medial graph $M(G)$.
+Figure~\ref{fig:whole-medial} draws all of $M(G)$ for the graph of
+Example~\ref{ex:real-cut}, with the tread $T_2$ of
+Figure~\ref{fig:real-cut} highlighted in place: its annular medial cycle
+in black, its up and down teeth in blue and red carrying their walk
+depths, and the remaining medial vertices---those outside any recognised
+tire---in grey.  This is the assembled cut graph emitted by the
+experiment: every recognised tread contributes its cuts, and the tire
+pieces are glued to the rest of $M(G)$ along their boundary medial
+vertices.
+
+\begin{figure}[h]
+\centering
+\input{whole_medial_seed72.tikz}
+\caption{The whole medial graph $M(G)$ of the random maximal planar graph
+on $20$ vertices from Example~\ref{ex:real-cut}, with all tire cuts
+applied.  Grey vertices are medial vertices outside any recognised tire;
+the highlighted tread $T_2$ (cf.\ Figure~\ref{fig:real-cut}) has black
+annular medial vertices, blue up-tooth and red down-tooth apexes carrying
+their walk depths, and the larger red vertex is the bite apex.  Drawn by
+\texttt{experiments/draw\_medial\_tire\_cut.py} with the \texttt{--whole}
+option.}
+\label{fig:whole-medial}
+\end{figure}
+
 \begin{thebibliography}{9}
 
 \bibitem{bauerfeld-medial-tire}