

\documentclass[addpoints,answers]{exam}

\usepackage{amsmath}
\usepackage{amssymb}    
\usepackage{amsfonts}
\usepackage{tikz}
\usepackage{verbatim}

\sloppy

\usetikzlibrary{arrows,shapes}

\tikzstyle{vertex}=[circle,fill=black,minimum size=3pt,inner sep=0pt]
\tikzstyle{edge} = [draw,thick,-]

\checkboxchar{$\Box$}
\checkedchar{$\blacksquare$}
\CorrectChoiceEmphasis{}


\begin{document}

    \pagestyle{headandfoot}
    \runningheadrule
    \firstpageheader{Math 184A}{Homework 5}{March 2, 2018}
    \runningheader{Math 184A}{Homework 5, Page \thepage\ of \numpages}{March 2, 2018}

    \firstpagefooter{}{}{}
    \runningfooter{}{}{}
    \begin{flushright}
        \makebox[0.4\textwidth]{Name:\enspace\hrulefill}

        \vspace{0.2in}

        \makebox[0.4\textwidth]{Pid:\enspace\hrulefill}
    \end{flushright}

    \begin{questions}
        \question
            Let $G$ be a graph on $n$ vertices such that every vertex has odd degree. Show
            that $n$ is even.
            \begin{solutionorbox}[\stretch{1}]
            \end{solutionorbox}
            \newpage
 
        \question
            Find a minimal $k(n)$ such that for every graph $G$ on $n$ vertices, if $G$ has
            at least $k(n)$ edges, then $G$ is connected.
            \begin{solutionorbox}[\stretch{1}]
            \end{solutionorbox}
            \newpage
 
        \question
            Let $G$ be a graph. Show that there are two different vertices $u$ and $v$ such
            that they have the same degree.
            \begin{solutionorbox}[\stretch{1}]
            \end{solutionorbox}
            \newpage
 
\end{questions}
\end{document}