Schlingen hinzugefügt; Textsetzungsprobleme behoben; Aufgabe 'Zeichne alle Graphen' verbessert

presentations/Diskrete-Mathematik/LaTeX/Grundlagen.tex

@@ -60,8 +60,25 @@ Hat eine Ecke den Grad 0, so nennt man ihn \textbf{isoliert}.
 \end{gallery}
 \end{frame}
 
+\begin{frame}{Schlinge}
+\begin{block}{Schlinge}
+Sei $G=(E, K)$ ein Graph und $k=\Set{e_1, e_2} \in K$ eine Kante.
+
+$k$ heißt \textbf{Schlinge} $:\Leftrightarrow e_1 = e_2$ 
+\end{block}
+
+Ein Graph ohne Schlingen heißt \enquote{schlingenfrei}
+
+\begin{gallery}
+    \galleryimage{graphs/graph-1}
+    \galleryimage{graphs/graph-2-schlinge}
+    \galleryimage{graphs/k-3-3}
+    \galleryimage{graphs/k-5-schlinge}
+\end{gallery}
+\end{frame}
+
 \begin{frame}{Aufgabe 1}
-Zeichnen Sie alle Graphen mit genau vier Ecken.
+Zeichnen Sie alle schlingenfreien Graphen mit genau vier Ecken.
 
 \only<2>{
     \begin{gallery}

presentations/Diskrete-Mathematik/LaTeX/graphs/graph-2-schlinge.tex

@@ -0,0 +1,29 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning} 
+\tikzset{
+    %Define standard arrow tip
+    >=stealth',
+    % Define arrow style
+    pil/.style={->,thick}
+}
+\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
+\begin{document}
+  \begin{tikzpicture}
+      \node (a)[vertex] at (0,3) {};
+      \node (b)[vertex] at (0,1) {};
+      \node (c)[vertex] at (1,0) {};
+      \node (d)[vertex] at (2,0) {};
+      \node (e)[vertex] at (3,0) {};
+      \node (f)[vertex] at (4,1) {};
+      \node (g)[vertex] at (4,3) {};
+
+      \foreach \from/\to in {b/c,c/d,d/e,e/f}
+        \draw[line width=2pt] (\from) -- (\to);
+
+        \path[line width=2pt] (d) edge[ out=140, in=50
+                , looseness=0.8, loop
+                , distance=2cm]
+            node[above=3pt] {$k$} (d);
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/graphs/k-5-schlinge.tex

@@ -0,0 +1,28 @@
+% A complete graph
+% Author: Quintin Jean-Noël
+% <http://moais.imag.fr/membres/jean-noel.quintin/>
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
+\usepackage{tikz}
+\usetikzlibrary[topaths]
+
+\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
+\begin{document}
+    \newcommand\n{5}
+    \begin{tikzpicture}
+        %the multiplication with floats is not possible. Thus I split the loop in two.
+        \foreach \number in {1,...,\n}{
+            \node[vertex] (N-\number) at ({\number*(360/\n)}:5.4cm) {};
+        }
+
+        \foreach \number in {1,...,\n}{
+            \foreach \y in {1,...,\n}{
+                \draw (N-\number) -- (N-\y);
+            }
+            \path (N-\number) edge[ out=140, in=50
+                    , looseness=0.8, loop
+                    , distance=2cm]
+                node[above=3pt] {} (N-\number);
+        }
+    \end{tikzpicture}
+\end{document}