Add subtree with hole figure

3 files changed, 72 insertions, 0 deletions

diff --git a/mgr.tex b/mgr.tex
index f7c66fd..ec250b6 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -1059,6 +1059,20 @@ components:
         doesn't lie on the $w$ to $v$ path.
 \end{itemize}
 
+\begin{figure}
+    \centering
+    \def\svgwidth{0.5\columnwidth}
+    \input{subtree-with-hole.pdf_tex}
+    \caption{
+        The subtree of $v$ with hole $w$. All its nodes can be partitioned into
+        the path $u_1, \ldots, u_4 = v$ and the subtrees of $u_1', \ldots,
+        u_4'$.
+    }\label{subtree-with-hole-figure}
+\end{figure}
+
+Figure \ref{subtree-with-hole-figure} depicts a subtree with hole labeled
+according to this nomenclature.
+
 With our bottom-up computation, we've already computed the new state in $w$.
 There have been no relabelings in the subtrees of the $u_i'$'s, so we can get
 their states from the precomputed run of $A$ on the original tree. Now consider
diff --git a/subtree-with-hole.pdf b/subtree-with-hole.pdf
new file mode 100644
index 0000000..50f5404
--- /dev/null
+++ b/subtree-with-hole.pdf
diff --git a/subtree-with-hole.pdf_tex b/subtree-with-hole.pdf_tex
new file mode 100644
index 0000000..ae74b70
--- /dev/null
+++ b/subtree-with-hole.pdf_tex
@@ -0,0 +1,58 @@
+%% Creator: Inkscape 1.1.1 (3bf5ae0d25, 2021-09-20, custom), www.inkscape.org
+%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
+%% Accompanies image file 'subtree-with-hole.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics{<filename>.pdf}
+%% To scale the image, write
+%%   \def\svgwidth{<desired width>}
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics[width=<desired width>]{<filename>.pdf}
+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
+%% installed) using
+%%   \usepackage{import}
+%% in the preamble, and then including the image with
+%%   \import{<path to file>}{<filename>.pdf_tex}
+%% Alternatively, one can specify
+%%   \graphicspath{{<path to file>/}}
+%% 
+%% For more information, please see info/svg-inkscape on CTAN:
+%%   http://tug.ctan.org/tex-archive/info/svg-inkscape
+%%
+\begingroup%
+  \makeatletter%
+  \providecommand\color[2][]{%
+    \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\transparent[1]{%
+    \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
+    \renewcommand\transparent[1]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \newcommand*\fsize{\dimexpr\f@size pt\relax}%
+  \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
+  \ifx\svgwidth\undefined%
+    \setlength{\unitlength}{734.22219354bp}%
+    \ifx\svgscale\undefined%
+      \relax%
+    \else%
+      \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
+    \fi%
+  \else%
+    \setlength{\unitlength}{\svgwidth}%
+  \fi%
+  \global\let\svgwidth\undefined%
+  \global\let\svgscale\undefined%
+  \makeatother%
+  \begin{picture}(1,0.9804307)%
+    \lineheight{1}%
+    \setlength\tabcolsep{0pt}%
+    \put(0,0){\includegraphics[width=\unitlength,page=1]{subtree-with-hole.pdf}}%
+  \end{picture}%
+\endgroup%