--- a/planarity/presentation.tex	Wed May 09 00:25:18 2012 +0200
+++ b/planarity/presentation.tex	Wed May 09 01:02:20 2012 +0200
@@ -49,8 +49,8 @@
 \tikzstyle{small vertex} = [vertex, minimum size=12pt]
 \tikzstyle{edge} = [draw,thick,-]
 \tikzstyle{tree edge} = [draw,very thick,->]
-\tikzstyle{left edge} = [draw,thick,->, red]
-\tikzstyle{right edge} = [draw,thick,->, blue]
+\tikzstyle{left edge} = [draw,thick,->, blue]
+\tikzstyle{right edge} = [draw,thick,->, red]
 \tikzstyle{back edge} = [draw,dashed,arrows={-latex}]
 \tikzstyle{selected edge} = [draw,line width=5pt,-,red!50]
 
@@ -666,82 +666,67 @@
 	\frametitle{Algorithmus}
 	
 	\begin{columns}[T]
-		\begin{column}{.6\textwidth}
-			\begin{columns}[T]
-				\begin{column}{.5\textwidth}
+		\begin{column}{.33\textwidth}
 	\begin{figure}
 	\begin{tikzpicture}[auto, scale=0.5]
-	\useasboundingbox (-5, 0) rectangle (5, 6);	
+	\useasboundingbox (-4, 0) rectangle (4, 9);	
+	
+	\node[small vertex] (u) at (0,3) {};
+	\node[small vertex] (v) at (0,6) {$v$};
+	\node[small vertex] (w) at (-2,8) {$w_1$};	
 	
-	\node[vertex] (u) at (0,0) {$u$};
-	\node[vertex] (v) at (0,3) {$v$};
-	\node[vertex] (w) at (-4,3) {$e_l^L$};
-	\node[vertex] (x) at (-3,5) {$e_2^L$};
-	\node[vertex] (y) at (-1,6) {$e_1^L$};		
-	\node[vertex] (a) at (1,6) {$e_1^R$};	
-	\node[vertex] (b) at (3,5) {$e_2^R$};	
-	\node[vertex] (c) at (4,3) {$e_r^R$};			
+	\path[edge] (u) -- (v);
+	\path[edge, ->] (v) -- (w);
+	\draw[edge] (0,0) -- (u);
+	\draw[edge] (v) -- (2, 8);
 	
-	\path[edge, ->] (u) -- (v);
-	\path[left edge] (v) -- (w);
-	\path[left edge] (v) -- (x);
-	\path[left edge] (v) -- (y);
-	\path[right edge] (v) -- (a);
-	\path[right edge] (v) -- (b);
-	\path[right edge] (v) -- (c);
+	\draw[left edge] (w) .. controls (-2, 5) .. (u);
+	\draw[back edge] (w) .. controls (-3, 5) .. (0,1);
 	
+	\draw[right edge] (2, 8) .. controls (2, 4) .. (0,2);
 	\end{tikzpicture}
 	\end{figure}				
 				\end{column}
-				\begin{column}{.5\textwidth}
+				\begin{column}{.33\textwidth}
 	\begin{figure}
 	\begin{tikzpicture}[auto, scale=0.5]
-	\useasboundingbox (-5, 0) rectangle (5, 6);	
+	\useasboundingbox (-4, 0) rectangle (4, 9);	
 	
-	\node[vertex] (u) at (0,0) {$u$};
-	\node[vertex] (v) at (0,3) {$v$};
-	\node[vertex] (w) at (-4,3) {$e_l^L$};
-	\node[vertex] (x) at (-3,5) {$e_2^L$};
-	\node[vertex] (y) at (-1,6) {$e_1^L$};		
-	\node[vertex] (a) at (1,6) {$e_1^R$};	
-	\node[vertex] (b) at (3,5) {$e_2^R$};	
-	\node[vertex] (c) at (4,3) {$e_r^R$};			
+	\node[small vertex] (u) at (0,3) {};
+	\node[small vertex] (v) at (0,6) {$v$};
+	\node[small vertex] (w) at (-2,8) {$w_1$};	
+	\node[small vertex] (x) at (2,8) {$w_2$};
 	
-	\path[edge, ->] (u) -- (v);
-	\path[left edge] (v) -- (w);
-	\path[left edge] (v) -- (x);
-	\path[left edge] (v) -- (y);
-	\path[right edge] (v) -- (a);
-	\path[right edge] (v) -- (b);
-	\path[right edge] (v) -- (c);
+	\path[edge] (u) -- (v);
+	\path[edge, ->] (v) -- (w);
+	\path[edge, ->] (v) -- (x);	
+	\draw[edge] (0,0) -- (u);
 	
+	\draw[left edge] (w) .. controls (-2, 5) .. (u);
+	\draw[right edge] (x) .. controls (2, 5) .. (u);
+	\draw[back edge] (w) .. controls (-3, 5) .. (-1,1);
+	\draw[back edge] (x) .. controls (3, 5) .. (1,1);	
 	\end{tikzpicture}
-	\end{figure}				
-				\end{column}
-			\end{columns}
+	\end{figure}	
 		\end{column}
-		\begin{column}{.4\textwidth}
+		\begin{column}{.33\textwidth}
 	\begin{figure}
 	\begin{tikzpicture}[auto, scale=0.5]
-	\useasboundingbox (-5, 0) rectangle (5, 6);	
+	\useasboundingbox (-4, 0) rectangle (4, 9);	
 	
-	\node[vertex] (u) at (0,0) {$u$};
-	\node[vertex] (v) at (0,3) {$v$};
-	\node[vertex] (w) at (-2,5) {$e^L$};
-	\node[vertex] (x) at (2, 5) {$e^R$};	
+	\node[small vertex] (u) at (0,3) {$v_2$};
+	\node[small vertex] (v) at (0,5) {$v_1$};
+	\node[small vertex] (w) at (0,7) {$x$};	
+	\node[small vertex] (x) at (0,9) {};
 	
-	\path[edge, ->] (u) -- (v);
-	\path[left edge] (v) -- (w);
-	\path[right edge] (v) -- (x);
+	\path[edge] (u) -- (v);
+	\path[edge] (v) -- (w);
+	\path[edge] (w) -- (x);	
+	\draw[edge] (0,0) -- (u);
 	
-	\draw[edge] (w) -- (-4,7);
-	\draw[left edge] (-4,7) .. controls(-4, 3.5) .. (v);
-	\draw[left edge] (-4,7) .. controls(-2.5, 3.5) .. (v);	
-	\draw[right edge] (-4,7) .. controls(-2, 7) .. (v);	
-	
-	\draw[edge] (x) -- (4,7);
-	\draw[left edge] (4,7) .. controls(4, 3.5) .. (v);	
-	\draw[right edge] (4,7) .. controls(2, 7) .. (v);	
+	\draw[right edge] (x) .. controls (3, 7) .. (u);
+	\draw[right edge] (x) .. controls (1.5, 7) .. (v);
+	\draw[back edge] (w) .. controls (-2, 5) .. (0,1);	
 	\end{tikzpicture}
 	\end{figure}	
 		\end{column}