2013-11-05 19:52:56 +01:00
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\subsection{Zweifachverbundener Graph}
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\begin{frame}{Zweifachverbundener Graph}{Biconnected graph}
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\begin{block}{Zweifachverbundener Graph}
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Ein Graph $G=(E,V)$ ist genau dann zweifach verbunden (engl. biconnected), wenn er keine Artikulationspunkte enthält.
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\end{block}
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Problem: Ist gegebener Graph zweifach verbunden? \\
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$\Rightarrow$ Suche nach Artikulationspunken!
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\end{frame}
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\begin{frame}{Beispiel}
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\begin{figure}
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\begin{tikzpicture}[scale=1.8, auto,swap]
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% Draw a 7,11 network
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% First we draw the vertices
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\foreach \pos/\name in {{(0,0)/a}, {(0,2)/b}, {(1,2)/c},
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2015-10-14 14:25:34 +02:00
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{(1,0)/d}, {(2,1)/e}, {(3,1)/f},
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2013-11-05 19:52:56 +01:00
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{(4,2)/g}, {(5,2)/h}, {(4,0)/i},
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{(5,0)/j}}
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\node[vertex] (\name) at \pos {$\name$};
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% Connect vertices with edges
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\foreach \source/ \dest /\pos in {a/b/,b/c/,c/d/,d/a/,
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d/e/,e/c/,
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e/f/,
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f/g/, f/i/,g/c/,
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g/h/, h/j/, j/i/, i/g/}
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\path (\source) edge [\pos] node {} (\dest);
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\end{tikzpicture}
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\end{figure}
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\end{frame}
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