diff --git a/report/img/refine_haystack_bad.png b/report/img/refine_haystack_bad.png
new file mode 100644
index 0000000..af93d38
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diff --git a/report/img/refine_haystack_ok.png b/report/img/refine_haystack_ok.png
new file mode 100644
index 0000000..932e93a
Binary files /dev/null and b/report/img/refine_haystack_ok.png differ
diff --git a/report/img/refine_needle.png b/report/img/refine_needle.png
new file mode 100644
index 0000000..e6a94fd
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diff --git a/report/img/ullmann_refine/haystack_bad.dot b/report/img/ullmann_refine/haystack_bad.dot
new file mode 100644
index 0000000..e3b7a8d
--- /dev/null
+++ b/report/img/ullmann_refine/haystack_bad.dot
@@ -0,0 +1,7 @@
+digraph haystack_bad {
+    a [style=filled, label=a’];
+    x -> a;
+    y -> a;
+    z -> x;
+    z -> y;
+}
diff --git a/report/img/ullmann_refine/haystack_ok.dot b/report/img/ullmann_refine/haystack_ok.dot
new file mode 100644
index 0000000..0d07431
--- /dev/null
+++ b/report/img/ullmann_refine/haystack_ok.dot
@@ -0,0 +1,9 @@
+digraph haystack_ok {
+    a [style=filled, label=a’];
+    x -> a;
+    y -> a;
+    z -> a;
+    y -> x;
+    y -> z;
+    z -> x;
+}
diff --git a/report/img/ullmann_refine/needle.dot b/report/img/ullmann_refine/needle.dot
new file mode 100644
index 0000000..ef468a1
--- /dev/null
+++ b/report/img/ullmann_refine/needle.dot
@@ -0,0 +1,6 @@
+digraph G {
+    a [style=filled];
+    b -> a;
+    c -> a;
+    b -> c;
+}
diff --git a/report/report.tex b/report/report.tex
index e5b13d9..2c6a3db 100644
--- a/report/report.tex
+++ b/report/report.tex
@@ -553,6 +553,18 @@ words, a match between $i$ and $j$ is only possible if every neighbour $k$ of
 $i$ (in needle) has a possibly matching (\wrt{} $perm$) vertex $k'$ (in
 haystack) which is a neighbour of $j$.
 
+For instance, for the needle from Figure~\ref{fig:refine_needle}'s, we can try
+to check the ones corresponding to the vertex $a$ (the coloured one).  Refining
+it while matching it with Figure~\ref{fig:refine_haystack_ok} will leave a $1$
+on the match $a-a'$, since every neighbour of $a$ can be matched with a
+neighbour of $a'$ (which, hopefully, are a $1$ in the matrix): $b$ matches $y$
+and $c$ matches $z$, for instance. It is not the case with the haystack from
+Figure~\ref{fig:refine_haystack_bad}: if the process went far enough already,
+there should be no corresponding vertex for either $b$ or $c$, since there are
+no such two vertices with an edge linking them. If there is indeed no match at
+this point for either $w$ or $c$, the $1$ in the cell matching $a - a'$ will be
+turned to a $0$.
+
 This condition is checked on every $1$ in the permutation matrix. If it is not
 met, the cell is nulled. This, though, potentially creates new ones not
 matching the condition: the process must be run again, until no new zeroes
@@ -565,7 +577,25 @@ of the adjacency of $j$ and the permutation matrix row of $k$.
 
 The refining function is detailed in Figure~\ref{alg:ullmann_refine}.
 
-\todo{Insert explaining figure}
+\begin{figure}[h]
+    \centering
+    \begin{minipage}{0.3\textwidth}
+        \centering
+        \includegraphics[width=0.5\textwidth]{img/refine_needle.png}
+        \caption{Needle}\label{fig:refine_needle}
+    \end{minipage}
+    \begin{minipage}{0.3\textwidth}
+        \centering
+        \includegraphics[width=0.5\textwidth]{img/refine_haystack_ok.png}
+        \caption{Matching haystack}\label{fig:refine_haystack_ok}
+    \end{minipage}
+    \begin{minipage}{0.3\textwidth}
+        \centering
+        \includegraphics[width=0.5\textwidth]{img/refine_haystack_bad.png}
+        \caption{Non-matching haystack}\label{fig:refine_haystack_bad}
+    \end{minipage}
+    \caption{Example: Ullmann refining process}
+\end{figure}
 
 \begin{figure}[h]
     \begin{algorithmic}