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.aux

@@ -24,4 +24,6 @@
 \@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}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The whole medial graph $M(G)$ of the random maximal planar graph on $20$ vertices from Example\nonbreakingspace 3.2\hbox {}, with all tire cuts applied. Grey vertices are medial vertices outside any recognised tire; the highlighted tread $T_2$ (cf.\ Figure\nonbreakingspace 2\hbox {}) 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.}}{5}{}\protected@file@percent }
+\newlabel{fig:whole-medial}{{3}{5}}
+\gdef \@abspage@last{5}