21 lines
1.9 KiB
TeX
21 lines
1.9 KiB
TeX
\relax
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\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Kempe's Proof (Valid Portion)}}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Setup}}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Every Planar Graph Has a Vertex of Degree at Most 5}}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Cases of Degree at Most 3}}{1}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.4}{Case of Degree 4}}{2}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Resolution of Degree 5 Case}}{2}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{At Least 12 Vertices of Degree 5}}{2}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Two Non-Adjacent Vertices of Degree 5}}{3}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.3}{The Reduced Subgraph $G'$}}{3}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.4}{Not All Colorings in $\Phi $ Saturate Both Neighborhoods}}{3}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Merged Subgraphs of $G'$}}{3}{}\protected@file@percent }
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\newlabel{tocindent-1}{0pt}
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\newlabel{tocindent0}{0pt}
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\newlabel{tocindent1}{17.77782pt}
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\newlabel{tocindent2}{29.38873pt}
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\newlabel{tocindent3}{0pt}
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Colorings of Merged Subgraphs Extend to $G'$}}{4}{}\protected@file@percent }
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\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{4-Saturating Merged Colorings Extend to 4-Saturating Colorings of $G'$}}{4}{}\protected@file@percent }
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\gdef \@abspage@last{4}
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