diff --git a/diagram_splittinglemma.tex b/diagram_splittinglemma.tex
new file mode 100644
index 0000000000000000000000000000000000000000..21a19b1e6255d2a620c429b3667b3194189537ee
--- /dev/null
+++ b/diagram_splittinglemma.tex
@@ -0,0 +1,56 @@
+\documentclass{standalone}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{parskip}
+\usepackage{marvosym} %Lightning symbol
+\usepackage[usenames,dvipsnames]{color}
+\usepackage[hidelinks]{hyperref}
+\renewcommand*{\familydefault}{\sfdefault}
+
+\usepackage{bbm} %For \mathbbm{1}
+%\usepackage{bbold}
+\usepackage{tikz}
+
+\begin{document}
+
+\begin{tikzpicture}[scale=0.8]
+    \def\width{6};
+    \def\height{4};
+    %\draw[step=1cm] (0,0) grid (\width,\height);
+
+    % Vertices and edges
+    \foreach \x in {0,...,\width} {
+        \foreach \y in {0,...,\height} {
+            \draw (\x,\y) circle (0.10);
+            \ifnum\x<\width
+                \draw (\x,\y)+(0.1,0) -- (\x+0.9,\y);
+            \fi
+            \ifnum\y<\height
+                \draw (\x,\y)+(0,0.1) -- (\x,\y+0.9);
+            \fi
+        }
+    }
+
+    %
+    % The set S : red circles
+    %
+
+    \draw[fill,red] (3,0) circle (0.08);
+    \draw[fill,red] (2,1) circle (0.08);
+    \draw[fill,red] (3,2) circle (0.08);
+    \draw[fill,red] (3,3) circle (0.08);
+    \draw[fill,red] (4,4) circle (0.08);
+
+    \draw (3,-0.5) node {$S$};
+
+    % The set X
+    \draw[xshift=-0.2cm,dashed] (-0.5,-1.0) -- (2.5,-1.0) -- (2.5,0.5) -- (1.5,0.5) -- (1.5,1.5) -- (2.5,1.5) -- (2.5,3.5) -- (3.5,3.5) -- (3.5,4.5) -- (-0.5,4.5) -- cycle;
+    \draw (1,-0.5) node {$X$};
+
+    % The set Y
+    \draw[xshift=+0.2cm,dashed] (6.5,-1.0) -- (3.5,-1.0) -- (3.5,0.5) -- (2.5,0.5) -- (2.5,1.5) -- (3.5,1.5) -- (3.5,3.5) -- (4.5,3.5) -- (4.5,4.5) -- (6.5,4.5) -- cycle;
+    \draw (5,-0.5) node {$Y$};
+
+\end{tikzpicture}
+\end{document}
