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\begin{document}
\title{Math 301 Homework}
\author{Mary Radcliffe}
\date{Due 1 December 2017}
\maketitle

Complete the following problems. Fully justify each response.

\begin{enumerate}

\item Complete problems 6, 8, 9, 16, 21 from \href{http://rellek.net/book/s_posets_exercises.html}{Applied Combinatorics} in Section 6.10.

\item A {\it vertex cover} in a graph is a set of vertices $S$ such that for every edge $e\in E$, at least one of the endpoints of $e$ is in $S$.

K\"onig's Theorem states the following:
\begin{quote}
If $G$ is a bipartite graph, then the size of a minimum vertex cover in $G$ is equal to the size of a maximum matching in $G$.
\end{quote}

Show that Hall's Theorem, K\"onig's Theorem, and Dilworth's Theorem are equivalent.
\end{enumerate}
\end{document}