\documentclass[12pt]{article}
\usepackage{fullpage}
\usepackage{epsfig}
\usepackage{latexsym}
\begin{document}
\begin{center}
\bf
Algorithms\\
Computer Science 140 \& Mathematics 168\\
Instructor: B. Thom\\
Fall 2003\\
\rm
Homework 11a\\
Due on 11/13/03 (in class)\\
\end{center}
\begin{enumerate}
\item \textbf{[14 Points] Review of Network Flow Proofs.}
In class we proved four fundamental theorems which, in the end, allowed us to show that
our network flow algorithm does indeed find a maximum flow from $s$ to $t$.  These four theorems were:

\begin{enumerate}
\item The Cut Theorem
\item The Capacity Theorem
\item The Max-Flow Min-Cut Theorem
\item The ``Greed is Good'' Theorem for Network Flows
\end{enumerate}

Note that our proofs and approach are easier than those given in the book.
Your task is to carefully write out the proofs for the first three of these theorems
{\bf as presented in class.}  
Your grade will be based largely on how clearly and precisely you write your proofs.








\end{enumerate}
\end{document}
