--- a/planarity/presentation.tex	Sun May 20 19:08:02 2012 +0200
+++ b/planarity/presentation.tex	Sun May 20 19:50:47 2012 +0200
@@ -477,8 +477,7 @@
         
     \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
         \path<3>[right edge] (\source) -- (\dest); 
-        
-    \draw<1> (0,0) node {Graph};                     
+                         
     \draw<2> (0,0) node {DFS};
     \draw<3> (0,0) node {LR-Partition};
 \end{tikzpicture}
@@ -732,10 +731,57 @@
 		\item Rückwärtskanten werden Knoten
 		\item Abhängigkeiten werden Kanten mit Beschriftung
 	\end{itemize}
+\end{frame}
+
+\begin{frame}
+	\frametitle{Constraintgraph}
 	
-	\begin{center}
-		Ich bin ein Constraintgraph
-	\end{center}
+\begin{figure}
+\begin{tikzpicture}[auto, scale=1.3]
+	\useasboundingbox (-4,1) rectangle (4,6);
+
+    \foreach \pos/\name in {{(0,1)/a},{(0,2)/b},{(1,3)/c},{(0.75,4)/d},{(-0.5,4.5)/e},
+                            {(-1.5,3.5)/f}, {(1.25,5.25)/g},
+                            {(0,5.5)/h}, {(2.5,6)/i}, {(4,5)/j},{(2.5,4.5)/k},
+                            {(-2,6)/l}, {(-2.5,5)/m}, {(-4,5)/n}}
+        \node<1>[small vertex] (\name) at \pos {$\name$};
+        
+    \foreach \source/ \dest in {a/b, b/c, c/d, d/e, e/f, e/g,
+                                e/h, h/i, i/j, j/k,
+                                h/l, l/m, m/n}
+        \path<1>[tree edge] (\source) -- (\dest);        
+                
+    \foreach \source/ \dest in {f/b, m/e, n/a}
+        \path<1>[left edge] (\source) -- (\dest);     
+        
+    \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
+        \path<1>[right edge] (\source) -- (\dest); 
+        
+    \foreach \pos/\name in {{(0,1)/a},{(0,2)/b},{(1,3)/c},{(0.75,4)/d},{(-0.5,4.5)/e},
+                            {(-1.5,3.5)/f}, {(1.25,5.25)/g},
+                            {(0,5.5)/h}, {(2.5,6)/i}, {(4,5)/j},{(2.5,4.5)/k},
+                            {(-2,6)/l}, {(-2.5,5)/m}, {(-4,5)/n}}
+        \node<2->[small vertex, draw opacity=0.2] (\name) at \pos {$\name$};
+        
+    \foreach \source/ \dest in {a/b, b/c, c/d, d/e, e/f, e/g,
+                                e/h, h/i, i/j, j/k,
+                                h/l, l/m, m/n}
+        \path<2->[tree edge, draw opacity=0.2] (\source) -- (\dest);        
+                
+    \foreach \source/ \dest / \name in {f/b, m/e, n/a}
+        \path<2->[left edge, draw opacity=0.2] (\source) -- (\dest)
+        		node[fill=blue,minimum size=10pt, midway, anchor=center, draw opacity=1] (\source\dest) {};     
+        
+    \foreach \source/ \dest in {k/c, k/i, j/a, g/d, n/l}
+        \path<2->[right edge, draw opacity=0.2] (\source) -- (\dest)
+        		node[fill=red,minimum size=10pt, midway, anchor=center, draw opacity=1] (\source\dest) {};
+        		
+    \path<3->[edge, ultra thick] (kc) -- (ki) node[midway] {s};
+    \path<4->[edge, ultra thick] (me) -- (nl) node[midway, above] {v};
+    \path<5->[edge, ultra thick] (me) -- (kc) node[midway] {v};
+    \path<5->[edge, ultra thick] (fb) -- (kc) node[midway] {v};        
+\end{tikzpicture}
+\end{figure}	
 \end{frame}
 
 \begin{frame}
@@ -752,7 +798,7 @@
 	
 	\vspace{0.5em}
 	\begin{itemize}
-		\item Erzeugen des Constraint Graphen hat eine Komplexität von $\Oh(n^2)$\\
+		\item Erzeugen des Constraint Graphen polynomieller Aufwand.
 		\item Kann in $\Oh(n)$ implementiert werden, indem der Graph nicht explizit erzeugt wird.
 	\end{itemize}
 \end{frame}