mirror of
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synced 2025-04-26 06:48:04 +02:00
added some images; devided big section into two sections
This commit is contained in:
Martin Thoma
parent
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commit
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21 changed files with 542 additions and 178 deletions
9
presentations/Diskrete-Mathematik/LaTeX/Ende.tex
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9
presentations/Diskrete-Mathematik/LaTeX/Ende.tex
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\subsection{Bildquelle}
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\begin{frame}{Bildquelle}
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\begin{itemize}
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\item \href{http://commons.wikimedia.org/wiki/File:Konigsberg\_bridges.png}{http://commons.wikimedia.org/wiki/File:Konigsberg\_bridges.png}
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\item \href{http://goo.gl/maps/WnXRh}{Google Maps} (Grafiken \TCop 2013 Cnes/Spot Image, DigitalGlobe)
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\end{itemize}
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\end{frame}
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Binary file not shown.
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@ -25,7 +25,13 @@
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\section{Grundlagen}
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\input{Grundlagen}
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\section{Spezielle Graphen}
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\input{Spezielle-Graphen}
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\section{Königsberger Brückenproblem}
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\input{Koenigsberger-Brueckenproblem}
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\section{Ende}
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\input{Ende}
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\end{document}
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@ -49,177 +49,3 @@ $e$ heißt \textbf{inzident} zu $k :\Leftrightarrow e = e_1$ oder $e = e_2$
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\galleryimage[Green]{inzidenz/tree}
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\end{gallery}
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\end{frame}
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\begin{frame}{Vollständige Graphen}
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\begin{block}{Vollständiger Graph}
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Sei $G = (E, K)$ ein Graph.
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$G$ heißt \textbf{vollständig} $:\Leftrightarrow = E \times E \setminus \Set{e \in E: \Set{e, e}}$
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\end{block}
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Ein vollständiger Graph mit $n$ Ecken wird als $K_n$ bezeichnet.
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\pause
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\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
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\begin{gallery}
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\galleryimage[Green]{vollstaendig/k-1}
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\galleryimage[Green]{vollstaendig/k-2}
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\galleryimage[Green]{vollstaendig/k-3}
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\galleryimage[Green]{vollstaendig/k-4}\\
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\galleryimage[Green]{vollstaendig/k-5}
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\galleryimage[Green]{vollstaendig/k-6}
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\galleryimage[Green]{vollstaendig/k-7}
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\galleryimage[Green]{vollstaendig/k-16}
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\end{gallery}
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\end{frame}
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\begin{frame}{Bipartite Graphen}
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\begin{block}{Bipartite Graph}
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Sei $G = (E, K)$ ein Graph und $A, B \subset V$ zwei disjunkte Eckenmengen mit
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$E \setminus A = B$.
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$G$ heißt \textbf{bipartit} $:\Leftrightarrow \forall_{k = \Set{e_1, e_2} \in K}: (e_1 \in A \text{ und } e_2 \in B) \text{ oder } (e_1 \in B \text{ und } e_2 \in A) $
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\end{block}
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TODO: 8 Bilder von Graphen
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\end{frame}
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\begin{frame}{Vollständig bipartite Graphen}
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\begin{block}{Vollständig bipartite Graphen}
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Sei $G = (E, K)$ ein bipartiter Graph und $\Set{A, B}$ bezeichne die Bipartition.
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$G$ heißt \textbf{vollständig bipartit} $:\Leftrightarrow \forall_{a \in A} \forall_{b \in B}: \Set{a, b} \in K$
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\end{block}
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\begin{gallery}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-2}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-3}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-3}\\
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\galleryimage[Green]{vollstaendig-bipartit/k-3-4}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-4-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-5-5}
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\end{gallery}
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\end{frame}
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\begin{frame}{Vollständig bipartite Graphen}
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Bezeichnung: Vollständig bipartite Graphen mit der Bipartition $\Set{A, B}$
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bezeichnet man mit $K_{|A|, |B|}$.
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\begin{gallery}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-2}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-3}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-3}\\
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\galleryimage[Green]{vollstaendig-bipartit/k-3-4}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-4-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-5-5}
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\end{gallery}
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\end{frame}
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\begin{frame}{Kantenzug}
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\begin{block}{Kantenzug}
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Sei $G = (E, K)$ ein Graph.
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Dann heißt eine Folge $k_1, k_2, \dots, k_s$ von Kanten, zu denen es Ecken
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$e_0, e_1, e_2, \dots, e_s$ gibt, so dass
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\begin{itemize}
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\item $k_1 = \Set{e_0, e_1}$
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\item $k_2 = \Set{e_1, e_2}$
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\item \dots
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\item $k_s = \Set{e_{s-1}, e_s}$
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\end{itemize}
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gilt ein \textbf{Kantenzug}, der \textcolor{purple}{$e_0$} und \textcolor{blue}{$e_s$} \textbf{verbindet} und $s$
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seine \textbf{Länge}.
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\end{block}
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\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
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\adjustbox{max size={\textwidth}{0.2\textheight}}{
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\begin{tikzpicture}
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\node (a)[vertex] at (1,1) {};
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\node (b)[vertex] at (2,5) {};
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\node (c)[vertex] at (3,3) {};
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\node (d)[vertex] at (5,4) {};
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\node (e)[vertex] at (3,6) {};
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\node (f)[vertex] at (5,6) {};
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\node (g)[vertex] at (7,6) {};
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\node (h)[vertex] at (7,4) {};
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\node (i)[vertex] at (6,2) {};
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\node (j)[vertex] at (8,7) {};
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\node (k)[vertex] at (9,5) {};
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\node (l)[vertex] at (13,6) {};
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\node (m)[vertex] at (11,7) {};
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\node (n)[vertex] at (15,7) {};
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\node (o)[vertex] at (16,4) {};
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\node (p)[vertex] at (10,2) {};
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\node (q)[vertex] at (13,1) {};
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\node (r)[vertex] at (16,1) {};
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\node (s)[vertex] at (17,4) {};
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\node (t)[vertex] at (19,6) {};
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\node (u)[vertex] at (18,3) {};
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\node (v)[vertex] at (20,2) {};
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\node (w)[vertex] at (15,4) {};
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\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}
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\draw[line width=2pt] (\from) -- (\to);
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\node (i)[vertex,purple] at (6,2) {};
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\node (v)[vertex,blue] at (20,2) {};
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\draw[line width=4pt, red] (i) -- (k) -- (l) -- (m) -- (n) -- (o) -- (t) -- (v);
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\end{tikzpicture}
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}
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\end{frame}
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\begin{frame}{Geschlossener Kantenzug}
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\begin{block}{Geschlossener Kantenzug}
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Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
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A heißt \textbf{geschlossen} $:\Leftrightarrow v_s = v_0$ .
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\end{block}
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TODO: 8 Bilder
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\end{frame}
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\begin{frame}{Weg}
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\begin{block}{Weg}
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Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
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A heißt \textbf{Weg} $:\Leftrightarrow \forall_{i, j \in [1, s] \cap \mathbb{N}}: i \neq j \Rightarrow e_i \neq e_j$ .
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\end{block}
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TODO: 8 Bilder
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\end{frame}
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\begin{frame}{Kreis}
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\begin{block}{Kreis}
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Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
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A heißt \textbf{Kreis} $:\Leftrightarrow A$ ist geschlossen und ein Weg.
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\end{block}
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TODO: 8 Bilder
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\end{frame}
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\begin{frame}{Zusammenhängender Graph}
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\begin{block}{Zusammenhängender Graph}
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Sei $G = (V, E)$ ein Graph.
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$G$ heißt \textbf{zusammenhängend} $:\Leftrightarrow \forall v_1, v_2 \in V: $ Es ex. ein Kantenzug, der $v_1$ und $v_2$ verbindet
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\end{block}
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TODO: 8 Bilder
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\end{frame}
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\begin{frame}{Grad einer Ecke}
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\begin{block}{Grad einer Ecke}
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Der \textbf{Grad} einer Ecke ist die Anzahl der Kanten, die von dieser Ecke
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ausgehen.
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\end{block}
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\begin{block}{Isolierte Ecken}
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Hat eine Ecke den Grad 0, so nennt man ihn \textbf{isoliert}.
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\end{block}
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TODO: 8 Bilder
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\end{frame}
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@ -1,10 +1,17 @@
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\subsection{Königsberger Brückenproblem}
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\begin{frame}{Königsberger Brückenproblem}
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TODO: Allgemeine Beschreibung
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\end{frame}
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\framedgraphic{Königsberg heute}{../images/koenigsberg-bruecken-luftbild}
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\framedgraphic{Königsberger Brückenproblem}{../images/Konigsberg_bridges.png}
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\framedgraphic{Übersetzung in einen Graphen}{../images/Konigsberg_bridges-graph.png}
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\begin{frame}{Übersetzung in einen Graphen}
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TODO: Übersetzung in Graph
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\begin{center}
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\adjustbox{max size={\textwidth}{0.8\textheight}}{
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\input{koenigsberg/koenigsberg-1}
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}
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\end{center}
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\end{frame}
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\begin{frame}{Eulerscher Kreis}
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219
presentations/Diskrete-Mathematik/LaTeX/Spezielle-Graphen.tex
Normal file
219
presentations/Diskrete-Mathematik/LaTeX/Spezielle-Graphen.tex
Normal file
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@ -0,0 +1,219 @@
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\subsection{Spezielle Graphen}
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\begin{frame}{Vollständige Graphen}
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\begin{block}{Vollständiger Graph}
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Sei $G = (E, K)$ ein Graph.
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$G$ heißt \textbf{vollständig} $:\Leftrightarrow = E \times E \setminus \Set{e \in E: \Set{e, e}}$
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\end{block}
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Ein vollständiger Graph mit $n$ Ecken wird als $K_n$ bezeichnet.
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\pause
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\tikzstyle{vertex}=[draw,fill=black,circle,minimum size=10pt,inner sep=0pt]
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\begin{gallery}
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\galleryimage[Green]{vollstaendig/k-1}
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\galleryimage[Green]{vollstaendig/k-2}
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\galleryimage[Green]{vollstaendig/k-3}
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\galleryimage[Green]{vollstaendig/k-4}\\
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\galleryimage[Green]{vollstaendig/k-5}
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\galleryimage[Green]{vollstaendig/k-6}
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\galleryimage[Green]{vollstaendig/k-7}
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\galleryimage[Green]{vollstaendig/k-16}
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\end{gallery}
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\end{frame}
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\begin{frame}{Bipartite Graphen}
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\begin{block}{Bipartite Graphen}
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Sei $G = (E, K)$ ein Graph und $A, B \subset V$ zwei disjunkte Eckenmengen mit
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$E \setminus A = B$.
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$G$ heißt \textbf{bipartit} $:\Leftrightarrow \forall_{k = \Set{e_1, e_2} \in K}: (e_1 \in A \text{ und } e_2 \in B) \text{ oder } (e_1 \in B \text{ und } e_2 \in A) $
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\end{block}
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\begin{gallery}
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\galleryimage[Green]{bipartit/k-2-2}
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\galleryimage[Green]{bipartit/k-2-3}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-3}\\
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\galleryimage[Green]{vollstaendig-bipartit/k-3-4}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-4-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-5-5}
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\end{gallery}
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\end{frame}
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\begin{frame}{Vollständig bipartite Graphen}
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\begin{block}{Vollständig bipartite Graphen}
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Sei $G = (E, K)$ ein bipartiter Graph und $\Set{A, B}$ bezeichne die Bipartition.
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$G$ heißt \textbf{vollständig bipartit} $:\Leftrightarrow \Set{\Set{a, b} | a \in A \land b \in B} = K$
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\end{block}
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\begin{gallery}
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\galleryimage[red]{bipartit/k-2-2}
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\galleryimage[red]{bipartit/k-2-3}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-3}\\
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\galleryimage[Green]{vollstaendig-bipartit/k-3-4}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-4-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-5-5}
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\end{gallery}
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\end{frame}
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\begin{frame}{Vollständig bipartite Graphen}
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Bezeichnung: Vollständig bipartite Graphen mit der Bipartition $\Set{A, B}$
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bezeichnet man mit $K_{|A|, |B|}$.
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\begin{gallery}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-2}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-3}
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\galleryimage[Green]{vollstaendig-bipartit/k-2-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-3}\\
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\galleryimage[Green]{vollstaendig-bipartit/k-3-4}
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\galleryimage[Green]{vollstaendig-bipartit/k-3-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-4-5}
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\galleryimage[Green]{vollstaendig-bipartit/k-5-5}
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\end{gallery}
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\end{frame}
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\begin{frame}{Kantenzug}
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\begin{block}{Kantenzug}
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Sei $G = (E, K)$ ein Graph.
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Dann heißt eine Folge $k_1, k_2, \dots, k_s$ von Kanten, zu denen es Ecken
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$e_0, e_1, e_2, \dots, e_s$ gibt, so dass
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\begin{itemize}
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\item $k_1 = \Set{e_0, e_1}$
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\item $k_2 = \Set{e_1, e_2}$
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\item \dots
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\item $k_s = \Set{e_{s-1}, e_s}$
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\end{itemize}
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gilt ein \textbf{Kantenzug}, der \textcolor{purple}{$e_0$} und \textcolor{blue}{$e_s$} \textbf{verbindet} und $s$
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seine \textbf{Länge}.
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\end{block}
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\adjustbox{max size={\textwidth}{0.2\textheight}}{
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\begin{tikzpicture}
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\node (a)[vertex] at (1,1) {};
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\node (b)[vertex] at (2,5) {};
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\node (c)[vertex] at (3,3) {};
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\node (d)[vertex] at (5,4) {};
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\node (e)[vertex] at (3,6) {};
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\node (f)[vertex] at (5,6) {};
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\node (g)[vertex] at (7,6) {};
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\node (h)[vertex] at (7,4) {};
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\node (i)[vertex] at (6,2) {};
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||||
\node (j)[vertex] at (8,7) {};
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\node (k)[vertex] at (9,5) {};
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\node (l)[vertex] at (13,6) {};
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\node (m)[vertex] at (11,7) {};
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\node (n)[vertex] at (15,7) {};
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\node (o)[vertex] at (16,4) {};
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\node (p)[vertex] at (10,2) {};
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\node (q)[vertex] at (13,1) {};
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\node (r)[vertex] at (16,1) {};
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\node (s)[vertex] at (17,4) {};
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\node (t)[vertex] at (19,6) {};
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\node (u)[vertex] at (18,3) {};
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\node (v)[vertex] at (20,2) {};
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\node (w)[vertex] at (15,4) {};
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\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}
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\draw[line width=2pt] (\from) -- (\to);
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\node (i)[vertex,purple] at (6,2) {};
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\node (v)[vertex,blue] at (20,2) {};
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\draw[line width=4pt, red] (i) -- (k) -- (l) -- (m) -- (n) -- (o) -- (t) -- (v);
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\end{tikzpicture}
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}
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\end{frame}
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||||
\begin{frame}{Geschlossener Kantenzug}
|
||||
\begin{block}{Geschlossener Kantenzug}
|
||||
Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
|
||||
|
||||
A heißt \textbf{geschlossen} $:\Leftrightarrow v_s = v_0$ .
|
||||
\end{block}
|
||||
|
||||
\begin{gallery}
|
||||
\galleryimage{walks/walk-1}
|
||||
\galleryimage{walks/walk-2}
|
||||
\galleryimage{walks/k-3-3-walk}
|
||||
\galleryimage{walks/k-5-walk}\\
|
||||
\galleryimage{walks/k-16-walk}
|
||||
\galleryimage{walks/star-graph-walk}
|
||||
\galleryimage{walks/tree-walk}
|
||||
\galleryimage{walks/walk-6}
|
||||
\end{gallery}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Weg}
|
||||
\begin{block}{Weg}
|
||||
Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
|
||||
|
||||
A heißt \textbf{Weg} $:\Leftrightarrow \forall_{i, j \in [1, s] \cap \mathbb{N}}: i \neq j \Rightarrow e_i \neq e_j$ .
|
||||
\end{block}
|
||||
|
||||
\pause
|
||||
|
||||
\begin{exampleblock}{Salopp}
|
||||
Ein Kantenzug, bei dem man keine Kante mehrfach abläuft, ist ein Weg.
|
||||
\end{exampleblock}
|
||||
|
||||
\pause
|
||||
|
||||
Achtung: Knoten dürfen mehrfach abgelaufen werden!
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Kreis}
|
||||
\begin{block}{Kreis}
|
||||
Sei $G = (V, E)$ ein Graph und $A = (e_1, e_2 \dots, e_s)$ ein Kantenzug.
|
||||
|
||||
A heißt \textbf{Kreis} $:\Leftrightarrow A$ ist geschlossen und ein Weg.
|
||||
\end{block}
|
||||
|
||||
\pause
|
||||
|
||||
Manchmal wird das auch "`einfacher Kreis"' genannt.
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Zusammenhängender Graph}
|
||||
\begin{block}{Zusammenhängender Graph}
|
||||
Sei $G = (V, E)$ ein Graph.
|
||||
|
||||
$G$ heißt \textbf{zusammenhängend} $:\Leftrightarrow \forall v_1, v_2 \in V: $ Es ex. ein Kantenzug, der $v_1$ und $v_2$ verbindet
|
||||
\end{block}
|
||||
|
||||
\begin{gallery}
|
||||
\galleryimage[red]{graphs/graph-1}
|
||||
\galleryimage[red]{graphs/graph-2}
|
||||
\galleryimage[Green]{graphs/k-3-3}
|
||||
\galleryimage[Green]{graphs/k-5}\\
|
||||
\galleryimage[Green]{graphs/k-16}
|
||||
\galleryimage[Green]{graphs/graph-6}
|
||||
\galleryimage[Green]{graphs/star-graph}
|
||||
\galleryimage[Green]{graphs/tree}
|
||||
\end{gallery}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Grad einer Ecke}
|
||||
\begin{block}{Grad einer Ecke}
|
||||
Der \textbf{Grad} einer Ecke ist die Anzahl der Kanten, die von dieser Ecke
|
||||
ausgehen.
|
||||
\end{block}
|
||||
|
||||
\begin{block}{Isolierte Ecken}
|
||||
Hat eine Ecke den Grad 0, so nennt man ihn \textbf{isoliert}.
|
||||
\end{block}
|
||||
|
||||
\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}
|
||||
16
presentations/Diskrete-Mathematik/LaTeX/bipartit/k-2-2.tex
Normal file
16
presentations/Diskrete-Mathematik/LaTeX/bipartit/k-2-2.tex
Normal file
|
|
@ -0,0 +1,16 @@
|
|||
\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}
|
||||
\foreach \y in {0,1}{
|
||||
\node (Node-0-\y)[vertexs] at (\y,0) {};
|
||||
\node (Node-\x-1)[vertexs] at (\x,1) {};
|
||||
}
|
||||
\draw (Node-0-1) -- (Node-1-1);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
16
presentations/Diskrete-Mathematik/LaTeX/bipartit/k-2-3.tex
Normal file
16
presentations/Diskrete-Mathematik/LaTeX/bipartit/k-2-3.tex
Normal file
|
|
@ -0,0 +1,16 @@
|
|||
\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}
|
||||
\foreach \y in {0,1,2}{
|
||||
\node (Node-0-\y)[vertexs] at (\y,0) {};
|
||||
\node (Node-\x-1)[vertexs] at (\x,1) {};
|
||||
}
|
||||
\draw (Node-0-1) -- (Node-1-1);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
|
@ -0,0 +1,21 @@
|
|||
\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 (0,8) {$a$};
|
||||
\node (b)[vertex] at (0,4) {$b$};
|
||||
\node (c)[vertex] at (0,0) {$c$};
|
||||
\node (d)[vertex] at (4,4) {$d$};
|
||||
|
||||
\foreach \from/\to/\pos in {a/b/20,a/b/-20,a/d/0,b/c/20,b/c/-20,b/d/0,c/d/0}
|
||||
\draw[line width=2pt] (\from) to [bend left=\pos] (\to);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
45
presentations/Diskrete-Mathematik/LaTeX/walks/k-16-walk.tex
Normal file
45
presentations/Diskrete-Mathematik/LaTeX/walks/k-16-walk.tex
Normal file
|
|
@ -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}
|
||||
20
presentations/Diskrete-Mathematik/LaTeX/walks/k-3-3-walk.tex
Normal file
20
presentations/Diskrete-Mathematik/LaTeX/walks/k-3-3-walk.tex
Normal file
|
|
@ -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}
|
||||
24
presentations/Diskrete-Mathematik/LaTeX/walks/k-5-walk.tex
Normal file
24
presentations/Diskrete-Mathematik/LaTeX/walks/k-5-walk.tex
Normal file
|
|
@ -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}
|
||||
|
|
@ -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[red] (N-0) -- (N-1);
|
||||
\draw[red] (N-0) -- (N-2);
|
||||
\draw (N-0) -- (N-3);
|
||||
\draw (N-0) -- (N-4);
|
||||
\draw (N-0) -- (N-5);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
36
presentations/Diskrete-Mathematik/LaTeX/walks/tree-walk.tex
Normal file
36
presentations/Diskrete-Mathematik/LaTeX/walks/tree-walk.tex
Normal file
|
|
@ -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[red] (a) -- (b);
|
||||
\draw[red] (a) -- (c);
|
||||
\draw[red] (b) -- (d);
|
||||
\draw[red] (b) -- (e);
|
||||
\draw[red] (b) -- (f);
|
||||
\draw[red] (d) -- (h);
|
||||
\draw[red] (d) -- (i);
|
||||
\draw[red] (c) -- (g);
|
||||
\draw (g) -- (j);
|
||||
\draw (g) -- (k);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
44
presentations/Diskrete-Mathematik/LaTeX/walks/walk-1.tex
Normal file
44
presentations/Diskrete-Mathematik/LaTeX/walks/walk-1.tex
Normal file
|
|
@ -0,0 +1,44 @@
|
|||
\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);
|
||||
|
||||
\node (i)[vertex,purple] at (6,2) {};
|
||||
\node (v)[vertex,blue] at (20,2) {};
|
||||
\draw[line width=4pt, red] (i) -- (k) -- (l) -- (m) -- (n) -- (o) -- (t) -- (v);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
24
presentations/Diskrete-Mathematik/LaTeX/walks/walk-2.tex
Normal file
24
presentations/Diskrete-Mathematik/LaTeX/walks/walk-2.tex
Normal file
|
|
@ -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/\color in {b/c/black,c/d/red,d/e/blue,e/f/lime}
|
||||
\draw[line width=2pt,\color] (\from) -- (\to);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
24
presentations/Diskrete-Mathematik/LaTeX/walks/walk-6.tex
Normal file
24
presentations/Diskrete-Mathematik/LaTeX/walks/walk-6.tex
Normal file
|
|
@ -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[red] (N-1) -- (N-2);
|
||||
\draw[red] (N-2) -- (N-3);
|
||||
\draw[red] (N-3) -- (N-4);
|
||||
\draw[red] (N-4) -- (N-5);
|
||||
\draw[red] (N-5) -- (N-1);
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
Loading…
Add table
Add a link
Reference in a new issue