\relax 
\citation{appel1977every}
\citation{robertson1997four}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{Notation}}{1}{}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Motivation}}{1}{}\protected@file@percent }
\citation{appel1977every}
\citation{robertson1997four}
\citation{mckaygraph6}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Definitions}}{2}{}\protected@file@percent }
\newlabel{def:distance-partition}{{2.1}{2}}
\newlabel{def:scaffold}{{2.2}{2}}
\newlabel{def:diamond}{{2.3}{2}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Results}}{2}{}\protected@file@percent }
\newlabel{thm:counterexample}{{3.3}{2}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The unique smallest maximal planar graph with no plane diamond coloring; it has $13$ vertices and degree sequence $(6,6,6,6,6,6,6,5,5,4,4,3,3)$.}}{3}{}\protected@file@percent }
\newlabel{fig:counterexample}{{1}{3}}
\newlabel{conj:mindeg5}{{3.4}{3}}
\newlabel{thm:mindeg5counterexample}{{3.5}{3}}
\bibcite{appel1977every}{1}
\bibcite{robertson1997four}{2}
\bibcite{mckaygraph6}{3}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{12.7778pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces One of four smallest counterexamples to Conjecture\nonbreakingspace 3.4\hbox {}: a maximal planar graph on $28$ vertices with minimum degree $5$ admitting no plane diamond coloring.}}{4}{}\protected@file@percent }
\newlabel{fig:mindeg5counterexample}{{2}{4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{4}{}\protected@file@percent }
\gdef \@abspage@last{4}
