From 422f732e62b027039d5820f42b8d10bd9da8afef Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Mon, 13 Dec 2021 16:28:40 +0100
Subject: Add partition figure

---
 mgr.tex           |  16 +++++++++++++++
 partition.pdf     | Bin 0 -> 6447 bytes
 partition.pdf_tex |  58 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 74 insertions(+)
 create mode 100644 partition.pdf
 create mode 100644 partition.pdf_tex

diff --git a/mgr.tex b/mgr.tex
index c26ae1a..4b4d025 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -869,6 +869,22 @@ singletons constructed according to the following rules:
         were assigned to parts when its children were handled.
 \end{enumerate}
 
+\begin{figure}
+    \centering
+    \def\svgwidth{\columnwidth}
+    \input{partition.pdf_tex}
+    \caption{
+        An LCA-partition of the tree with respect to the black vertices. The
+        dark grey vertices are added when computing the LCA closure, the light
+        grey vertices are the final vertices needed to create a minimal
+        partition ready set containing the black vertices. Part (a) is an
+        example of a singleton, part (b) of a subtree with a hole, and (c) of a
+        subtree.
+    }\label{partition-figure}
+\end{figure}
+
+See Figure \ref{partition-figure} for an example of a partitioned tree.
+
 If $W$ is not parition ready, we will define the LCA partition with respect to
 $W$ the partition with respect to the minimal partition ready set that contains
 $W$. Skipping ahead, the LCA partition of the set of vertices relabeled in a
diff --git a/partition.pdf b/partition.pdf
new file mode 100644
index 0000000..953ca4c
Binary files /dev/null and b/partition.pdf differ
diff --git a/partition.pdf_tex b/partition.pdf_tex
new file mode 100644
index 0000000..b5de94f
--- /dev/null
+++ b/partition.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 'partition.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}{439.05363307bp}%
+    \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}(1,0.52063675)%
+    \lineheight{1}%
+    \setlength\tabcolsep{0pt}%
+    \put(0,0){\includegraphics[width=\unitlength,page=1]{partition.pdf}}%
+  \end{picture}%
+\endgroup%
-- 
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