added examples to presentation

presentations/Diskrete-Mathematik/LaTeX/Graphentheorie-I.tex

@@ -2,7 +2,6 @@
 \usepackage{../templates/myStyle}
 
 \begin{document}
-%\selectlanguage{english}
 
 \title{\titleText}
 \subtitle{}

presentations/Diskrete-Mathematik/LaTeX/Grundlagen.tex

@@ -5,18 +5,49 @@ Ein Graph ist ein Tupel $(V, E)$, wobei $V \neq \emptyset$ die Knotenmenge und
 $E \subseteq V \times V$ die 
 Kantenmenge bezeichnet.
 \end{block}
+\pause
+\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
+
+\begin{gallery}
+    \galleryimage{graphs/graph-1}
+    \galleryimage{graphs/graph-2}
+    \galleryimage{graphs/k-3-3}
+    \galleryimage{graphs/k-5}\\
+    \galleryimage{graphs/k-16}
+    \galleryimage{graphs/graph-6}
+    \galleryimage{graphs/star-graph}
+    \galleryimage{graphs/tree}
+\end{gallery}
+\end{frame}
+
+\begin{frame}{Synonyme}
+
+\begin{center}
+\Huge{Knoten $\Leftrightarrow$ Ecken}
+\end{center}
 
-TODO: 8 Bilder von Graphen
 \end{frame}
 
 \begin{frame}{Inzidenz}
 \begin{block}{Inzidenz}
-Sei $v \in V$ und $e = (v_1, v_2) \in E$.
+Sei $v \in V$ und $e = \Set{v_1, v_2} \in E$.
 
 $v$ heißt \textbf{inzident} zu $e :\Leftrightarrow v = v_1$ oder $v = v_2$
 \end{block}
 
-TODO: 8 Bilder von Graphen
+\pause
+\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
+
+\begin{gallery}
+    \galleryimage{inzidenz/graph-1}
+    \galleryimage{inzidenz/graph-2}
+    \galleryimage{inzidenz/k-3-3}
+    \galleryimage{inzidenz/k-5}\\
+    \galleryimage{inzidenz/k-16}
+    \galleryimage{inzidenz/graph-6}
+    \galleryimage{inzidenz/star-graph}
+    \galleryimage{inzidenz/tree}
+\end{gallery}
 \end{frame}
 
 \begin{frame}{Vollständige Graphen}
@@ -26,10 +57,19 @@ Sei $G = (V, E)$ ein Graph.
 $G$ heißt \textbf{vollständig} $:\Leftrightarrow E = V \times V \setminus \Set{v \in V: \Set{v, v}}$
 \end{block}
 
-Ein vollständiger Graphen mit $n$ Knoten wird als $K_n$ bezeichnet.
-
-TODO: 8 Bilder von Graphen
-TODO: $K_1, K_2, ... K_8$
+Ein vollständiger Graph mit $n$ Knoten wird als $K_n$ bezeichnet.
+\pause
+\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
+\begin{gallery}
+    \galleryimage{vollstaendig/k-1}
+    \galleryimage{vollstaendig/k-2}
+    \galleryimage{vollstaendig/k-3}
+    \galleryimage{vollstaendig/k-4}\\
+    \galleryimage{vollstaendig/k-5}
+    \galleryimage{vollstaendig/k-6}
+    \galleryimage{vollstaendig/k-7}
+    \galleryimage{vollstaendig/k-16}
+\end{gallery}
 \end{frame}
 
 \begin{frame}{Bipartite Graphen}

presentations/Diskrete-Mathematik/LaTeX/graphs/graph-1.tex

@@ -0,0 +1,40 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning} 
+\tikzset{
+    %Define standard arrow tip
+    >=stealth',
+    % Define arrow style
+    pil/.style={->,thick}
+}
+
+\begin{document}
+  \begin{tikzpicture}
+      \node (a)[vertex] at (1,1) {};
+      \node (b)[vertex] at (2,5) {};
+      \node (c)[vertex] at (3,3) {};
+      \node (d)[vertex] at (5,4) {};
+      \node (e)[vertex] at (3,6) {};
+      \node (f)[vertex] at (5,6) {};
+      \node (g)[vertex] at (7,6) {};
+      \node (h)[vertex] at (7,4) {};
+      \node (i)[vertex] at (6,2) {};
+      \node (j)[vertex] at (8,7) {};
+      \node (k)[vertex] at (9,5) {};
+      \node (l)[vertex] at (13,6) {};
+      \node (m)[vertex] at (11,7) {};
+      \node (n)[vertex] at (15,7) {};
+      \node (o)[vertex] at (16,4) {};
+      \node (p)[vertex] at (10,2) {};
+      \node (q)[vertex] at (13,1) {};
+      \node (r)[vertex] at (16,1) {};
+      \node (s)[vertex] at (17,4) {};
+      \node (t)[vertex] at (19,6) {};
+      \node (u)[vertex] at (18,3) {};
+      \node (v)[vertex] at (20,2) {};
+      \node (w)[vertex] at (15,4) {};
+
+      \foreach \from/\to in {a/c,c/b,c/d,d/f,f/g,g/h,h/d,d/g,h/f,i/k,k/j,k/l,l/m,m/n,n/o,o/t,t/v,v/u,s/r,o/q,q/p,u/t}
+        \draw[line width=2pt] (\from) -- (\to);
+  \end{tikzpicture}
+\end{document}

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

@@ -0,0 +1,24 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning} 
+\tikzset{
+    %Define standard arrow tip
+    >=stealth',
+    % Define arrow style
+    pil/.style={->,thick}
+}
+
+\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);
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/graphs/graph-6.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\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) {};
+        }
+
+        \draw (N-1) -- (N-2);
+        \draw (N-2) -- (N-3);
+        \draw (N-3) -- (N-4);
+        \draw (N-4) -- (N-5);
+        \draw (N-5) -- (N-1);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/graphs/k-16.tex

@@ -0,0 +1,45 @@
+% A complete graph
+% Author: Quintin Jean-Noël
+% <http://moais.imag.fr/membres/jean-noel.quintin/>
+\documentclass[varwidth=true, border=2pt]{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary[topaths]
+
+
+\begin{document}
+
+% A counter, since TikZ is not clever enough (yet) to handle
+% arbitrary angle systems.
+\newcount\mycount
+
+  \tikzstyle{vertexs}=[draw,fill=black,circle,minimum size=4pt,inner sep=0pt]
+
+  \begin{tikzpicture}
+      %the multiplication with floats is not possible. Thus I split the loop in two.
+      \foreach \number in {1,...,8}{
+          % Computer angle:
+            \mycount=\number
+            \advance\mycount by -1
+      \multiply\mycount by 45
+            \advance\mycount by 0
+          \node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
+        }
+      \foreach \number in {9,...,16}{
+          % Computer angle:
+            \mycount=\number
+            \advance\mycount by -1
+      \multiply\mycount by 45
+            \advance\mycount by 22.5
+          \node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
+        }
+      \foreach \number in {1,...,15}{
+            \mycount=\number
+            \advance\mycount by 1
+      \foreach \numbera in {\the\mycount,...,16}{
+        \path (N-\number) edge[->,bend right=3] (N-\numbera)  edge[<-,bend
+          left=3] (N-\numbera);
+      }
+    }
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/graphs/k-3-3.tex

@@ -0,0 +1,20 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning}
+
+\begin{document}
+  \tikzstyle{vertexs}=[draw,fill=black,circle,minimum size=4pt,inner sep=0pt]
+
+  \begin{tikzpicture}
+    \foreach \x in {0,1,2}
+    \foreach \y in {0,1,2}{
+      \node (a)[vertexs] at (\y,0) {};
+      \node (b)[vertexs] at (\x,1) {};
+        \draw (a) -- (b);
+    }
+  %  \foreach \x in {0,1,2}{
+  %      \draw (\x,0) circle (2pt);
+  %      \draw (\x,1) circle (2pt);
+  %  }
+  \end{tikzpicture}
+\end{document}

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

@@ -0,0 +1,24 @@
+% 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]
+
+
+\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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/graphs/star-graph.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{5}
+    \begin{tikzpicture}
+        \node[vertex] (N-0) at (0:0) {};
+        \foreach \number in {1,...,\n}{
+            \node[vertex] (N-\number) at ({\number*(360/\n)}:5.4cm) {};
+        }
+
+        \draw (N-0) -- (N-1);
+        \draw (N-0) -- (N-2);
+        \draw (N-0) -- (N-3);
+        \draw (N-0) -- (N-4);
+        \draw (N-0) -- (N-5);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/graphs/tree.tex

@@ -0,0 +1,36 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{5}
+    \begin{tikzpicture}
+        \node[vertex] (a) at (3,6) {};
+        \node[vertex] (b) at (2,4) {};
+        \node[vertex] (c) at (4,4) {};
+        \node[vertex] (d) at (1,2) {};
+        \node[vertex] (e) at (2,2) {};
+        \node[vertex] (f) at (3,2) {};
+        \node[vertex] (g) at (4,2) {};
+        \node[vertex] (h) at (0,0) {};
+        \node[vertex] (i) at (2,0) {};
+        \node[vertex] (j) at (3,0) {};
+        \node[vertex] (k) at (5,0) {};
+
+        \draw (a) -- (b);
+        \draw (a) -- (c);
+        \draw (b) -- (d);
+        \draw (b) -- (e);
+        \draw (b) -- (f);
+        \draw (d) -- (h);
+        \draw (d) -- (i);
+        \draw (c) -- (g);
+        \draw (g) -- (j);
+        \draw (g) -- (k);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/graph-1.tex

@@ -0,0 +1,40 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning} 
+\tikzset{
+    %Define standard arrow tip
+    >=stealth',
+    % Define arrow style
+    pil/.style={->,thick}
+}
+
+\begin{document}
+  \begin{tikzpicture}
+      \node (a)[vertex] at (1,1) {};
+      \node (b)[vertex] at (2,5) {};
+      \node (c)[vertex] at (3,3) {};
+      \node (d)[vertex] at (5,4) {};
+      \node (e)[vertex] at (3,6) {};
+      \node (f)[vertex] at (5,6) {};
+      \node (g)[vertex] at (7,6) {};
+      \node (h)[vertex] at (7,4) {};
+      \node (i)[vertex] at (6,2) {};
+      \node (j)[vertex] at (8,7) {};
+      \node (k)[vertex] at (9,5) {};
+      \node (l)[vertex] at (13,6) {};
+      \node (m)[vertex] at (11,7) {};
+      \node (n)[vertex] at (15,7) {};
+      \node (o)[vertex] at (16,4) {};
+      \node (p)[vertex] at (10,2) {};
+      \node (q)[vertex] at (13,1) {};
+      \node (r)[vertex] at (16,1) {};
+      \node (s)[vertex] at (17,4) {};
+      \node (t)[vertex] at (19,6) {};
+      \node (u)[vertex] at (18,3) {};
+      \node (v)[vertex] at (20,2) {};
+      \node (w)[vertex,purple] at (15,4) {};
+
+      \foreach \from/\to in {a/c,c/b,c/d,d/f,f/g,g/h,h/d,d/g,h/f,i/k,k/j,k/l,l/m,m/n,n/o,o/t,t/v,v/u,s/r,o/q,q/p,u/t}
+        \draw[line width=2pt] (\from) -- (\to);
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/graph-2.tex

@@ -0,0 +1,26 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning} 
+\tikzset{
+    %Define standard arrow tip
+    >=stealth',
+    % Define arrow style
+    pil/.style={->,thick}
+}
+
+\begin{document}
+  \begin{tikzpicture}
+      \node (a)[vertex] at (0,3) {};
+      \node (b)[vertex] at (0,1) {};
+      \node (c)[vertex,red] 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);
+      \draw[line width=2pt,green] (c) -- (b);
+      \draw[line width=2pt,green] (c) -- (d);
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/graph-6.tex

@@ -0,0 +1,27 @@
+% 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]
+
+
+\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) {};
+        }
+
+        \node[vertex] (N-3) at ({3*(360/\n)}:5.4cm) {};
+        \node[vertex] (N-4) at ({4*(360/\n)}:5.4cm) {};
+
+        \draw (N-1) -- (N-2);
+        \draw (N-2) -- (N-3);
+        \draw[green, ultra thick] (N-3) -- (N-4);
+        \draw (N-4) -- (N-5);
+        \draw (N-5) -- (N-1);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/k-16.tex

@@ -0,0 +1,63 @@
+% A complete graph
+% Author: Quintin Jean-Noël
+% <http://moais.imag.fr/membres/jean-noel.quintin/>
+\documentclass[varwidth=true, border=2pt]{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary[topaths]
+
+
+\begin{document}
+
+% A counter, since TikZ is not clever enough (yet) to handle
+% arbitrary angle systems.
+\newcount\mycount
+
+  \tikzstyle{vertexs}=[draw,fill=black,circle,minimum size=4pt,inner sep=0pt]
+
+  \begin{tikzpicture}
+      %the multiplication with floats is not possible. Thus I split the loop in two.
+      \foreach \number in {1,...,8}{
+          % Computer angle:
+            \mycount=\number
+            \advance\mycount by -1
+      \multiply\mycount by 45
+            \advance\mycount by 0
+          \node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
+        }
+      \foreach \number in {9,...,16}{
+          % Computer angle:
+            \mycount=\number
+            \advance\mycount by -1
+      \multiply\mycount by 45
+            \advance\mycount by 22.5
+          \node[draw,circle,inner sep=0.25cm] (N-\number) at (\the\mycount:5.4cm) {};
+        }
+      \foreach \number in {1,...,15}{
+            \mycount=\number
+            \advance\mycount by 1
+      \foreach \numbera in {\the\mycount,...,16}{
+        \path (N-\number) edge[->,bend right=3] (N-\numbera)  edge[<-,bend
+          left=3] (N-\numbera);
+      }
+    }
+
+
+    \node[draw,circle,inner sep=0.25cm,red,fill] (N-0) at (0:5.4cm) {};
+    \draw[green, ultra thick] (N-1) -- (N-2);
+    \draw[green, ultra thick] (N-1) -- (N-3);
+    \draw[green, ultra thick] (N-1) -- (N-4);
+    \draw[green, ultra thick] (N-1) -- (N-5);
+    \draw[green, ultra thick] (N-1) -- (N-6);
+    \draw[green, ultra thick] (N-1) -- (N-7);
+    \draw[green, ultra thick] (N-1) -- (N-8);
+    \draw[green, ultra thick] (N-1) -- (N-9);
+    \draw[green, ultra thick] (N-1) -- (N-10);
+    \draw[green, ultra thick] (N-1) -- (N-11);
+    \draw[green, ultra thick] (N-1) -- (N-12);
+    \draw[green, ultra thick] (N-1) -- (N-13);
+    \draw[green, ultra thick] (N-1) -- (N-14);
+    \draw[green, ultra thick] (N-1) -- (N-15);
+    \draw[green, ultra thick] (N-1) -- (N-16);
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/k-3-3.tex

@@ -0,0 +1,19 @@
+\documentclass[varwidth=true, border=2pt]{standalone}
+\usepackage{tikz}
+\usetikzlibrary{arrows,positioning}
+
+\begin{document}
+  \tikzstyle{vertexs}=[draw,fill=black,circle,minimum size=4pt,inner sep=0pt]
+
+  \begin{tikzpicture}
+    \foreach \x in {0,1,2}
+    \foreach \y in {0,1,2}{
+      \node (a)[vertexs] at (\y,0) {};
+      \node (b)[vertexs] at (\x,1) {};
+        \draw (a) -- (b);
+    }
+    \draw[green,ultra thick] (1,1) -- (0,0);
+    \node (b)[vertexs,red] at (1,1) {};
+    \node (b)[vertexs,red] at (0,0) {};
+  \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/k-5.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]
+
+
+\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);
+            }
+        }
+
+        \node[vertex,red] (N-3) at ({3*(360/\n)}:5.4cm) {};
+        \node[vertex,red] (N-5) at ({5*(360/\n)}:5.4cm) {};
+        \draw[green, ultra thick] (N-3) -- (N-5);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/star-graph.tex

@@ -0,0 +1,27 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{5}
+    \begin{tikzpicture}
+        \node[vertex] (N-0) at (0:0) {};
+        \foreach \number in {1,...,\n}{
+            \node[vertex] (N-\number) at ({\number*(360/\n)}:5.4cm) {};
+        }
+
+        \node[vertex,red] (N-0) at (0,0) {};
+        \node[vertex,red] (N-4) at ({4*(360/\n)}:5.4cm) {};
+
+        \draw (N-0) -- (N-1);
+        \draw (N-0) -- (N-2);
+        \draw (N-0) -- (N-3);
+        \draw[green,ultra thick] (N-0) -- (N-4);
+        \draw (N-0) -- (N-5);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/inzidenz/tree.tex

@@ -0,0 +1,36 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{5}
+    \begin{tikzpicture}
+        \node[vertex] (a) at (3,6) {};
+        \node[vertex,red] (b) at (2,4) {};
+        \node[vertex] (c) at (4,4) {};
+        \node[vertex] (d) at (1,2) {};
+        \node[vertex] (e) at (2,2) {};
+        \node[vertex,red] (f) at (3,2) {};
+        \node[vertex] (g) at (4,2) {};
+        \node[vertex] (h) at (0,0) {};
+        \node[vertex] (i) at (2,0) {};
+        \node[vertex] (j) at (3,0) {};
+        \node[vertex] (k) at (5,0) {};
+
+        \draw (a) -- (b);
+        \draw (a) -- (c);
+        \draw (b) -- (d);
+        \draw (b) -- (e);
+        \draw[green,ultra thick] (b) -- (f);
+        \draw (d) -- (h);
+        \draw (d) -- (i);
+        \draw (c) -- (g);
+        \draw (g) -- (j);
+        \draw (g) -- (k);
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-1.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{1}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-16.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{16}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-2.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{2}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-3.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{3}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-4.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{4}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-5.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-6.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{6}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}

presentations/Diskrete-Mathematik/LaTeX/vollstaendig/k-7.tex

@@ -0,0 +1,24 @@
+% 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]
+
+
+\begin{document}
+    \newcommand\n{7}
+    \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);
+            }
+        }
+    \end{tikzpicture}
+\end{document}