\relax \citation{bauerfeld-medial-tire} \citation{bauerfeld-medial-tire} \citation{bauerfeld-medial-tire} \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent } \@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} \bibcite{bauerfeld-medial-tire}{1} \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}