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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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\@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 }
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\@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 }
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