\relax 
\citation{bauerfeld-nested-tire-decompositions}
\citation{bauerfeld-nested-tire-decompositions}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Background}}{1}{}\protected@file@percent }
\citation{bauerfeld-nested-tire-decompositions}
\citation{bauerfeld-nested-tire-decompositions}
\newlabel{def:medial-graph}{{2.1}{2}}
\newlabel{prop:medial-dual-invariance}{{2.3}{2}}
\newlabel{cor:tait-medial}{{2.4}{2}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Medial tire pieces}}{2}{}\protected@file@percent }
\newlabel{def:full-medial-tire}{{3.1}{2}}
\newlabel{thm:annular-medial-colour-bound}{{3.3}{3}}
\newlabel{def:boundary-medial-vertices}{{3.4}{3}}
\newlabel{def:medial-restriction-relation}{{3.5}{3}}
\citation{bauerfeld-nested-tire-decompositions}
\citation{bauerfeld-nested-tire-decompositions}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Decomposition}}{4}{}\protected@file@percent }
\newlabel{cor:medial-tire-decomposition}{{4.1}{4}}
\newlabel{def:compatible-family}{{4.2}{4}}
\newlabel{prop:gluing-criterion}{{4.3}{4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{A medial pigeonhole programme}}{4}{}\protected@file@percent }
\bibcite{bauerfeld-nested-tire-decompositions}{1}
\bibcite{tait-original}{2}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\newlabel{def:medial-boundary-state}{{5.1}{5}}
\newlabel{conj:medial-chain-pigeonhole}{{5.2}{5}}
\newlabel{conj:medial-route-fct}{{5.3}{5}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{5}{}\protected@file@percent }
\gdef \@abspage@last{5}