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version={3.0}, +]{doclicense} + +\title{Zusammenfassung Diskrete Mathematik} +\author{Marcel Schneider} + +\begin{document} + +\maketitle +\tableofcontents +\bigskip + +\section{Graphentheorie} + \subsection{Kreis}\label{graph:kreis} + Ein geschlossener Kantenzug mit $k_1, k_2, \dots, k_s$, der die Ecken $e_1, e_2,\ldots,e_s=e_0$ miteinander verbindet. + Alle Kanten müssen dabei unterschiedlich sein. + Die Länge des Kreises beschreibt die Anzahl der Kanten oder Ecken. + + \subsection{Eulerscher Kreis}\label{graph:eulerschKreis} + Ein \nameref{graph:kreis} $C$ in einem Graph $G$ heißt eulersch, wenn jede Kante aus G in ihm genau einmal vorkommt. + + \subsection{Eulerscher Graph}\label{graph:eulersch} + Ein Graph heißt eulersch, wenn er einen \hyperref[subsec:eulerschKreis]{eulerschen Kreis} besitzt. + Jede Ecke eines eulerschen Graphen hat geraden Grad. + Besitzt also eine Ecke des Graphen ungeraden Grad, so ist es kein eulerscher Graph. + + \subsection{Zusammenhangskomponente}\label{graph:komponente} + Ein maximaler, zusammenhängender Teilgraph $G^*$ von eines Graphen $G$. + +\vspace*{\fill} % show license on bottom of page +\doclicenseThis{} +\end{document}