\relax \citation{bauerfeld-depth} \citation{bauerfeld-depth} \citation{bauerfeld-depth} \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Motivation}}{1}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Preliminaries from plane depth}}{1}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Quadrilateral sequencing}}{2}{}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The deep embedding $G'$ of a small maximal planar graph (drawn with one outer-cap face as the outer face), with each quadrilateral $Q_n$ of the canonical sequence labelled by its index and the move code (AD = anchor drop, LA = level add, J = join, RC = ring completion) of the move that produced it. Solid edges are non-level; dashed edges are level. Background colour encodes quadrilateral type: amber for shallow diamonds, teal for deep diamonds, pink for S quads. Outer-cycle vertices are blue, the outer-cap vertex $x^{*}$ is red. The move-code string for this example is $01211333$.}}{4}{}\protected@file@percent } \newlabel{fig:example-sequence}{{1}{4}} \bibcite{bauerfeld-depth}{1} \newlabel{tocindent-1}{0pt} \newlabel{tocindent0}{12.7778pt} \newlabel{tocindent1}{17.77782pt} \newlabel{tocindent2}{0pt} \newlabel{tocindent3}{0pt} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{6}{}\protected@file@percent } \gdef \@abspage@last{6}