\relax 
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Motivation}}{1}{}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Preliminaries}}{1}{}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces An edge flip replaces the diagonal $uv$ of the quadrilateral $uwvx$ with the diagonal $wx$.}}{2}{}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Flip neighborhoods and colored edge flip classes}}{2}{}\protected@file@percent }
\newlabel{def:flip-neighborhood}{{3.1}{2}}
\newlabel{def:colored-flip-class}{{3.2}{2}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{The flip neighborhood of a minimum-order counterexample}}{2}{}\protected@file@percent }
\newlabel{def:edge-deletion}{{4.1}{2}}
\newlabel{lem:edge-deletion-4colorable}{{4.2}{2}}
\newlabel{lem:edge-deletion-coloring-structure}{{4.3}{3}}
\newlabel{thm:flip-neighborhood-4colorable}{{4.4}{3}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{0pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Case\nonbreakingspace 2 of the proof of Theorem\nonbreakingspace 4.4\hbox {}: $u, v$ share color $a$ and $w, x$ share color $c$. The $\{a, b\}$-Kempe path $P$ from $u$ to $v$ separates $w$ from $x$ in the plane, so no $\{c, d\}$-path between $w$ and $x$ can avoid crossing $P$; since the color sets $\{a, b\}$ and $\{c, d\}$ are disjoint, no such path exists.}}{4}{}\protected@file@percent }
\newlabel{fig:flip-proof-case-two}{{2}{4}}
\newlabel{thm:no-colored-class-contains-G}{{4.5}{4}}
\gdef \@abspage@last{4}
