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math-research/papers/level_resolutions_of_maximal_planar_graphs/paper-old.aux
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didericis bd9c46d3e4 Add level resolutions of maximal planar graphs paper
Migrate the paper content into the amsart template and include the
supporting experiments scripts.
2026-05-19 23:35:01 -04:00

49 lines
3.0 KiB
TeX

\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}{\numberline {1}Introduction}{1}{section.1}\protected@file@percent }
\citation{chartrand}
\@writefile{toc}{\contentsline {section}{\numberline {2}Definitions}{2}{section.2}\protected@file@percent }
\newlabel{def:resolution}{{4}{2}{Level resolution}{definition.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {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}{{1}{2}{}{proposition.1}{}}
\newlabel{prop:bipartite-suffices}{{2}{3}{}{proposition.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}The four-color conjecture via level resolutions}{3}{section.4}\protected@file@percent }
\newlabel{conj:preimage}{{1}{3}{Resolution preimage}{conjecture.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Computational evidence}{3}{section.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {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}{{1}{3}{}{observation.1}{}}
\@writefile{toc}{\contentsline {paragraph}{Equivalence to 4-colorability.}{4}{section*.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Surjectivity at $n = 12$: the icosahedron}{4}{subsection.5.2}\protected@file@percent }
\newlabel{obs:icosa}{{2}{4}{}{observation.2}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Restatement of the resolution-preimage conjecture}{4}{subsection.5.3}\protected@file@percent }
\newlabel{conj:md4}{{2}{4}{$\mathrm {md}_4$ surjectivity}{conjecture.2}{}}
\@writefile{toc}{\contentsline {section}{\numberline {6}Discussion and open questions}{4}{section.6}\protected@file@percent }
\bibcite{appelhaken}{1}
\bibcite{rsst}{2}
\bibcite{tutte}{3}
\bibcite{chartrand}{4}
\@writefile{toc}{\contentsline {section}{\numberline {7}Implementation}{5}{section.7}\protected@file@percent }
\newlabel{sec:impl}{{7}{5}{Implementation}{section.7}{}}
\gdef \@abspage@last{5}