From 4014f044ef3c91f84047b851989a27774f44565f Mon Sep 17 00:00:00 2001 From: Never Gude Date: Fri, 17 Apr 2026 14:40:08 +0200 Subject: [PATCH] Initial commit --- übung_1/ads_übung_1.aux | 21 + übung_1/ads_übung_1.fdb_latexmk | 176 ++++ übung_1/ads_übung_1.fls | 176 ++++ übung_1/ads_übung_1.log | 1380 ++++++++++++++++++++++++++++++ übung_1/ads_übung_1.pdf | Bin 0 -> 28941 bytes übung_1/ads_übung_1.synctex.gz | Bin 0 -> 6712 bytes übung_1/ads_übung_1.tex | 52 ++ übung_1/agt26-blatt01.pdf | Bin 0 -> 99371 bytes übung_1/msb-eps-converted-to.pdf | Bin 0 -> 3745 bytes übung_1/msb.eps | 180 ++++ übung_1/msb.ipe | 691 +++++++++++++++ 11 files changed, 2676 insertions(+) create mode 100644 übung_1/ads_übung_1.aux create mode 100644 übung_1/ads_übung_1.fdb_latexmk create mode 100644 übung_1/ads_übung_1.fls create mode 100644 übung_1/ads_übung_1.log create mode 100644 übung_1/ads_übung_1.pdf create mode 100644 übung_1/ads_übung_1.synctex.gz create mode 100644 übung_1/ads_übung_1.tex create mode 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Übungsblatt} +\subject{Algorithmische Graphentheorie} +\author{Jasper Gude} + +\begin{document} +\maketitle +\points[\qquad]{20} +\section{Spannbäume \& Breitensuche} +Sei $G = \tup{V, E}$ ein zusammenhängender Graph mit Kantengewichten $w: E \to \NN$ +und $s \in V \deg$ ein ausgezeichneter Knoten. +\begin{enumerate} + \item + \begin{quote} + Wenn $w(e) = 1$ für alle $e \in E$, dann ist der Breitensuchbaum mit + Quelle $s$ ein minimaler Spannbaum. + \end{quote} + Die Breitensuche berechnet in diesem + Fall den kürzesten Weg von jedem Knoten zum Knoten $s$, also den + Breitensuchbaum. Dieser spannt also einen minimalen Spannbaum auf. + \points{2} + \item + \begin{quote} + Wenn $w(e) = 1$ für alle $e \in E$, dann ist jeder minimale Spannbaum + von $G$ ein Breitensuchbaum mit Quelle $s$. + \end{quote} + Falsch, siehe \autoref{fig:msb}. + \begin{figure}[h] + \centering + \includegraphics[width=0.2\textwidth]{msb.eps} + \caption{$\pi$-Zeiger des Breitensuchbaums und MSB blau hinterlegt.} + \label{fig:msb} + \end{figure} + \item + \begin{quote} + Wenn $w(e) \in \set{1, 2, 3}$ für alle $e \in E$, dann ist jeder minimale + Spannbaum von $G$ ein Tiefensuchbaum mit Quelle $s$. + \end{quote} + Sei $w(e) = 1$ für + alle $e \in E$ so gilt das Gegenbeispiel von oben. Also ist die Aussage + falsch. +\end{enumerate} + +\section{Kreissuche} + +\section{Eulerwege} + +\section{Graphmodellierung} + +\end{document} diff --git a/übung_1/agt26-blatt01.pdf b/übung_1/agt26-blatt01.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b2703326ab376bd3b112cbb4c6e8611ef44976b2 GIT binary patch literal 99371 zcma&NQ?qbEn{Bym+qP}nwr$&Zw{6?DZQHhOtH0CH)o~)KE-J4w*AG}@4XO7_-GN?Pr6zHt63yNfl0Y(B0`pB{(LMMHIuXX$b!A1w|O zu?|0bb{3il2`eO5cQ^OPX>=e@u^%|2SVnZePos$gGPSD-o?mNZ&38zZZN$=jz^UqPk%W0w~3_ADPUfTH&MvU_r7ps6#3} zkrEl8QcjbT)rERd3FKiia107f=}Q6mxLNuypxvdy}0 z_ZS)lTJP++133UhdWYv&wM78om7D!6@43T5W+9{UCN2MLq4wdR7V#Rpfx>a1gCPqH zPz#Zu1;V~sQNV{Ku9RZS`O|wk3lpah_ov1JDePsd+y8t%Db-P*eI~lBpySRW--4UG zfNVOy8fbjcM$e`LD;%1+EdkKB!$`_<@zsF7p0lpCgLhdVtB{E{L7l?GF!Hs4!E_3Y z6GQuE_Be*p;eCajk^gxntRtDJnbkKhHsM$07>3%O) zRf{*PP@n4re^~0!I2FSGJ}ctF!>Fw&pv^883%cIiMoTk+1Oa%iHL}}!V5trJ$)sO9 z<${L6@V>Kh!2L)D#F7=cVJME9^&@I1225DXlYdIYf-3Jz@J5`TtdtNn6PX}$Ob3{P 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