diff --git a/übung_1/agt_übung_1.aux b/übung_1/agt_übung_1.aux index a93da76..50c2411 100644 --- a/übung_1/agt_übung_1.aux +++ b/übung_1/agt_übung_1.aux @@ -8,14 +8,16 @@ \providecommand\HyField@AuxAddToCoFields[2]{} \providecommand\BKM@entry[2]{} \BKM@entry{id=1,dest={73656374696F6E2E31},srcline={10},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C303030535C303030705C303030615C3030306E5C3030306E5C303030625C3030305C3334345C303030755C3030306D5C303030655C3030305C3034305C3030305C3034365C3030305C3034305C303030425C303030725C303030655C303030695C303030745C303030655C3030306E5C303030735C303030755C303030635C303030685C30303065} -\BKM@entry{id=2,dest={73656374696F6E2E32},srcline={50},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C3030304B5C303030725C303030655C303030695C303030735C303030735C303030755C303030635C303030685C30303065} +\BKM@entry{id=2,dest={73656374696F6E2E32},srcline={57},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C3030304B5C303030725C303030655C303030695C303030735C303030735C303030755C303030635C303030685C30303065} \babel@aux{ngerman}{} \@writefile{toc}{\contentsline {section}{\numberline {1}Spannbäume \& Breitensuche}{1}{section.1}\protected@file@percent } \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces $\mitpi $-Zeiger des Breitensuchbaums und MSB blau hinterlegt.}}{1}{figure.1}\protected@file@percent } \newlabel{fig:msb}{{1}{1}{$\pi $-Zeiger des Breitensuchbaums und MSB blau hinterlegt}{figure.1}{}} -\BKM@entry{id=3,dest={73656374696F6E2E33},srcline={128},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C303030455C303030755C3030306C5C303030655C303030725C303030775C303030655C303030675C30303065} +\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Tiefensuchbaum in orange und MSB blau hinterlegt.}}{2}{figure.2}\protected@file@percent } +\newlabel{fig:dfs}{{2}{2}{Tiefensuchbaum in orange und MSB blau hinterlegt}{figure.2}{}} \@writefile{toc}{\contentsline {section}{\numberline {2}Kreissuche}{2}{section.2}\protected@file@percent } -\BKM@entry{id=4,dest={73656374696F6E2E34},srcline={154},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C303030475C303030725C303030615C303030705C303030685C3030306D5C3030306F5C303030645C303030655C3030306C5C3030306C5C303030695C303030655C303030725C303030755C3030306E5C30303067} +\BKM@entry{id=3,dest={73656374696F6E2E33},srcline={135},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C303030455C303030755C3030306C5C303030655C303030725C303030775C303030655C303030675C30303065} +\BKM@entry{id=4,dest={73656374696F6E2E34},srcline={161},srcfile={2F686F6D652F6E657665722F446F63756D656E74732F496E4E612F32365F536F53652F4147542F6167745F65786572636973652FFC62756E675F312F6167745FFC62756E675F312E746578}}{5C3337365C3337375C303030475C303030725C303030615C303030705C303030685C3030306D5C3030306F5C303030645C303030655C3030306C5C3030306C5C303030695C303030655C303030725C303030755C3030306E5C30303067} \@writefile{toc}{\contentsline {section}{\numberline {3}Eulerwege}{3}{section.3}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {4}Graphmodellierung}{3}{section.4}\protected@file@percent } -\gdef \@abspage@last{3} +\gdef \@abspage@last{4} diff --git a/übung_1/agt_übung_1.fdb_latexmk b/übung_1/agt_übung_1.fdb_latexmk index 6c58aed..9217161 100644 --- a/übung_1/agt_übung_1.fdb_latexmk +++ b/übung_1/agt_übung_1.fdb_latexmk @@ -1,5 +1,5 @@ # Fdb version 4 -["lualatex"] 1776687964.3922 "/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/agt_übung_1.tex" "agt_übung_1.pdf" "agt_übung_1" 1776687966.21834 0 +["lualatex"] 1776689922.84723 "/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/agt_übung_1.tex" "agt_übung_1.pdf" "agt_übung_1" 1776689924.63041 0 "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/euler-math.luc" 1770519352.28514 417132 89f085d929a7f52a226e499fed2b660f "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/lmroman10-bold.luc" 1770519351.28214 128405 86240d2e88c12243734a13e4bf6704ec "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/lmroman10-regular.luc" 1770519350.86413 127322 64667bb671c8def3fa5d85c341ebd817 "" @@ -17,7 +17,7 @@ "/home/never/.texlive2025/texmf-var/luatex-cache/generic/fonts/otl/texgyrepagella-regular.luc" 1770519351.40914 310182 64e3ff98a9959bea5d737ee8b9a06ff2 "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/names/luaotfload-lookup-cache.luc" 1776608606.25376 23014 4a1f49530b644afddd7c9abad44fb6f5 "" "/home/never/.texlive2025/texmf-var/luatex-cache/generic/names/luaotfload-names.luc.gz" 1770519350.80013 381420 8c34679872cd58fe28bd24cc6f0940ba "" - "/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/agt_übung_1.tex" 1776687963.64524 5687 f4492753592b18742dd16079aa201ada "" + "/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/agt_übung_1.tex" 1776689920.30511 5918 404e74808326e7cb118bd3c5e2c239db "" "/home/never/texmf/tex/latex/ngexrcs/ngexrcs.cls" 1776614186.59271 2041 f7d79ac75cecdfbe676fa2a93e60930b "" "/home/never/texmf/tex/latex/ngutils/ngutils.sty" 1776618253.70411 4493 7f39562722b52c0e9a76c17c4438174e "" "/usr/local/texlive/2025/texmf-dist/fonts/opentype/public/euler-math/Euler-Math.otf" 1761682777 433104 26cb5ed06a913ce89a33ff41234f5c7a "" @@ -171,8 +171,9 @@ "/usr/local/texlive/2025/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1770517628 5541377 824b1e5beafd2ebda40585373b35bb6b "" "/usr/local/texlive/2025/texmf-var/tex/generic/config/language.dat" 1770517624.99251 6800 99336720d16c8191172704bea65615e7 "" "/usr/local/texlive/2025/texmf-var/web2c/luahbtex/lualatex.fmt" 1770517696 5655839 756767735d369e65a483b47207bff649 "" - "agt_übung_1.aux" 1776687965.9159 2666 9cc8dc5483982b638424f38dffb2e051 "lualatex" - "agt_übung_1.tex" 1776687963.64524 5687 f4492753592b18742dd16079aa201ada "" + "agt_übung_1.aux" 1776689924.38713 2915 9d880eef7bcc0cb3af62e0b7eba25b39 "lualatex" + "agt_übung_1.tex" 1776689920.30511 5918 404e74808326e7cb118bd3c5e2c239db "" + "dfs.eps" 1776689817.37668 5896 bfdfa03e5701d0b1d7555aa426023dcf "" "msb.eps" 1776424417.18606 5913 81dafb89427e3a448260b7481993e119 "" (generated) "agt_übung_1.aux" diff --git a/übung_1/agt_übung_1.fls b/übung_1/agt_übung_1.fls index 4672b31..7799f3d 100644 --- a/übung_1/agt_übung_1.fls +++ b/übung_1/agt_übung_1.fls @@ -176,5 +176,7 @@ INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/cm/cmmi10.tfm INPUT /usr/local/texlive/2025/texmf-dist/fonts/tfm/public/cm/cmmi7.tfm INPUT ./msb-eps-converted-to.pdf INPUT ./msb-eps-converted-to.pdf +INPUT ./dfs-eps-converted-to.pdf +INPUT ./dfs-eps-converted-to.pdf INPUT /usr/local/texlive/2025/texmf-var/fonts/map/pdftex/updmap/pdftex.map INPUT ./agt_übung_1.aux diff --git a/übung_1/agt_übung_1.log b/übung_1/agt_übung_1.log index 4fe2d0e..cc39179 100644 --- a/übung_1/agt_übung_1.log +++ b/übung_1/agt_übung_1.log @@ -1,4 +1,4 @@ -This is LuaHBTeX, Version 1.22.0 (TeX Live 2025) (format=lualatex 2026.2.8) 20 APR 2026 14:26 +This is LuaHBTeX, Version 1.22.0 (TeX Live 2025) (format=lualatex 2026.2.8) 20 APR 2026 14:58 restricted system commands enabled. **/home/never/Documents/InNa/26_SoSe/AGT/agt_exercise/übung_1/agt_übung_1.tex @@ -1379,24 +1379,42 @@ File: msb-eps-converted-to.pdf Graphic file (type pdf) Package luatex.def Info: msb-eps-converted-to.pdf used on input line 35. (luatex.def) Requested size: 71.69984pt x 74.25963pt. +Package epstopdf Info: Source file: +(epstopdf) date: 2026-04-20 14:56:57 +(epstopdf) size: 5896 bytes +(epstopdf) Output file: +(epstopdf) date: 2026-04-20 14:57:58 +(epstopdf) size: 3721 bytes +(epstopdf) Command: +(epstopdf) \includegraphics on input line 50. +Package epstopdf Info: Output file is already uptodate. + +File: dfs-eps-converted-to.pdf Graphic file (type pdf) + +Package luatex.def Info: dfs-eps-converted-to.pdf used on input line 50. +(luatex.def) Requested size: 71.69984pt x 73.23537pt. + + +LaTeX Warning: `h' float specifier changed to `ht'. [1 {/usr/local/texlive/2025/texmf-var/fonts/map/pdftex/updmap/pdftex.map}<./msb-eps --converted-to.pdf>] [2] -Overfull \hbox (2.21837pt too wide) in paragraph at lines 146--148 +-converted-to.pdf>] [2<./dfs-eps-converted-to.pdf>] +Overfull \hbox (2.21837pt too wide) in paragraph at lines 153--155 \TU/TeXGyrePagella(0)/m/n/10.95 kann nicht exis-tie-ren, da die Sum-me al-ler Kn o-ten mit un-ge-ra-dem Grad [] -Overfull \hbox (2.02118pt too wide) in paragraph at lines 156--162 +Overfull \hbox (2.02118pt too wide) in paragraph at lines 163--169 \TU/TeXGyrePagella(0)/m/n/10.95 wer-den, wenn be-stimm-te an-de-re Auf-ga-ben ab - ge-schlos-sen sind. [] -[3] (./agt_übung_1.aux) +[3] [4] (./agt_übung_1.aux) *********** LaTeX2e <2025-11-01> L3 programming layer <2026-01-19> @@ -1404,15 +1422,15 @@ L3 programming layer <2026-01-19> ) Here is how much of LuaTeX's memory you used: - 22896 strings out of 476076 + 22908 strings out of 476076 100000,1373583 words of node,token memory allocated 3192 words of node memory still in use: 61 hlist, 40 vlist, 38 rule, 9 local_par, 78 glue, 31 kern, 9 penalty, 20 gly ph, 213 attribute, 62 glue_spec, 107 attribute_list, 1 write nodes - avail lists: 1:1,2:660,3:277,4:4,5:380,6:50,7:4204,8:16,9:451,10:4,11:416 - 45012 multiletter control sequences out of 65536+600000 - 118 fonts using 28706639 bytes - 122i,8n,114p,11297b,573s stack positions out of 10000i,1000n,20000p,200000b,200000s + avail lists: 1:1,2:655,3:303,4:4,5:433,6:52,7:4721,8:16,9:476,10:4,11:478 + 45020 multiletter control sequences out of 65536+600000 + 118 fonts using 28706879 bytes + 122i,8n,114p,11297b,574s stack positions out of 10000i,1000n,20000p,200000b,200000s -Output written on agt_übung_1.pdf (3 pages, 46777 bytes). +Output written on agt_übung_1.pdf (4 pages, 48895 bytes). -PDF statistics: 118 PDF objects out of 1000 (max. 8388607) - 83 compressed objects within 1 object stream - 15 named destinations out of 1000 (max. 131072) +PDF statistics: 132 PDF objects out of 1000 (max. 8388607) + 94 compressed objects within 1 object stream + 17 named destinations out of 1000 (max. 131072) 33 words of extra memory for PDF output out of 10000 (max. 100000000) diff --git a/übung_1/agt_übung_1.pdf b/übung_1/agt_übung_1.pdf index d8c55a0..4ed4906 100644 Binary files a/übung_1/agt_übung_1.pdf and b/übung_1/agt_übung_1.pdf differ diff --git a/übung_1/agt_übung_1.synctex.gz b/übung_1/agt_übung_1.synctex.gz index 18c8a71..4a0257b 100644 Binary files a/übung_1/agt_übung_1.synctex.gz and b/übung_1/agt_übung_1.synctex.gz differ diff --git a/übung_1/agt_übung_1.tex b/übung_1/agt_übung_1.tex index 8d4d35d..a2e5d4f 100644 --- a/übung_1/agt_übung_1.tex +++ b/übung_1/agt_übung_1.tex @@ -42,8 +42,15 @@ Falsch, siehe \autoref{fig:msb}. 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} -Gegenbeispiel siehe Foto +Falsch, siehe \autoref{fig:dfs}. Der Minimale Spannbaum kann kein Tiefensuchbaum +sein. \points{2} +\begin{figure}[h] + \centering + \includegraphics[width=0.2\textwidth]{dfs.eps} + \caption{Tiefensuchbaum in orange und MSB blau hinterlegt.} + \label{fig:dfs} +\end{figure} \end{tasks}