\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\citation{appelhaken}
\citation{rsst}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}{section.1}\protected@file@percent }
\citation{chartrand}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Definitions}}{2}{section.2}\protected@file@percent }
\newlabel{def:resolution}{{2.4}{2}{Level resolution}{theorem.2.4}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Structural foundation: outerplanarity of level subgraphs}}{2}{section.3}\protected@file@percent }
\newlabel{sec:outerplanar}{{3}{2}{Structural foundation: outerplanarity of level subgraphs}{section.3}{}}
\newlabel{prop:outerplanar}{{3.1}{2}{}{theorem.3.1}{}}
\newlabel{prop:bipartite-suffices}{{3.2}{2}{}{theorem.3.2}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The four-color conjecture via level resolutions}}{3}{section.4}\protected@file@percent }
\newlabel{conj:preimage}{{4.1}{3}{Resolution preimage}{theorem.4.1}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Computational evidence}}{3}{section.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Coverage at $n = 6, \ldots  , 11$}}{3}{subsection.5.1}\protected@file@percent }
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Iso-class coverage under the level-resolution definition.}}{3}{table.1}\protected@file@percent }
\newlabel{tab:coverage}{{1}{3}{Iso-class coverage under the level-resolution definition}{table.1}{}}
\newlabel{obs:preimage}{{5.1}{3}{}{theorem.5.1}{}}
\@writefile{toc}{\contentsline {paragraph}{\tocparagraph {}{}{Equivalence to 4-colorability.}}{3}{section*.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Surjectivity at $n = 12$: the icosahedron}}{4}{subsection.5.2}\protected@file@percent }
\newlabel{obs:icosa}{{5.2}{4}{}{theorem.5.2}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{Restatement of the resolution-preimage conjecture}}{4}{subsection.5.3}\protected@file@percent }
\newlabel{conj:md4}{{5.3}{4}{$\mathrm {md}_4$ surjectivity}{theorem.5.3}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Discussion and open questions}}{4}{section.6}\protected@file@percent }
\bibcite{appelhaken}{1}
\bibcite{rsst}{2}
\bibcite{tutte}{3}
\bibcite{chartrand}{4}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{29.38873pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Implementation}}{5}{section.7}\protected@file@percent }
\newlabel{sec:impl}{{7}{5}{Implementation}{section.7}{}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{5}{section*.2}\protected@file@percent }
\gdef \@abspage@last{5}