% To print single-sided: delete ",twoside" below
\documentclass[11pt,twoside]{article}

% Some very basic packages. Feel free to add your favorites!
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{fancyhdr}
\usepackage{graphicx}

% Set up the page correctly
\addtolength{\oddsidemargin}{-.54in}
\addtolength{\evensidemargin}{-1.2in}
\addtolength{\textwidth}{1.75in}
\addtolength{\topmargin}{-.875in}
\addtolength{\textheight}{1.75in}
\setlength{\parindent}{0pt}
\setlength{\parskip}{5pt plus 1pt}

% Some nifty commands. Thanks Adam Blank!
\newcommand{\question}[2] {\vspace{.25in} \hrule\vspace{0.5em}
\noindent{{\bf #1:} #2} \vspace{0.5em}
\hrule \vspace{.10in}}
\renewcommand{\part}[1] {\vspace{.10in} {\bf (#1)}}

% Add an image centered on the page.
% The first parameter is a scale factor (set to 1 for no scale)
% The second parameter is the image file. Make sure it is in the same folder as your .tex file!
\newcommand{\centergfx}[2]{\begin{center}\includegraphics[scale = #1]{#2}\end{center}}

% Command to insert a minus sign with a dot over it. Stolen from
% http://www.cs.miami.edu/~burt/learning/Math688.931/Other/errata.tex
\newcommand{\monus}{\stackrel{{}^{\scriptstyle .}}{\smash{-}}}

%%%%%%%%%%%%%%%%%%%%%
%		Replace "Name" and                 %
%		   "andrewid" below                   %
%%%%%%%%%%%%%%%%%%%%%
\newcommand{\myname}{Name}
\newcommand{\myandrew}{(andrewid)}
\newcommand{\mysection}{ - X}
\newcommand{\myhwnum}{6}
\newcommand{\myclass}{21-484 Graph Theory}

% Set up the nice header
\pagestyle{fancyplain}
\lhead{\fancyplain{}{\textbf{HW\myhwnum}}}
\rhead{\fancyplain{}{\myname \ \myandrew \ \mysection}}
\chead{\fancyplain{}{\myclass}}

\begin{document}
% Question 1
\question{1}{Draw $K^7$ on a torus with no edge crossings.}

\cleardoublepage

% Question 2
\question{2}{Find a $TK^5$ or a $TK_{3,3}$ in the Petersen Graph.}

\cleardoublepage

% Question 3
\question{3, Diestel 4.4}{Show that every planar graph is a union of three forests.}

\cleardoublepage

\question{4, Diestel 4.23}{A graph is called \emph{outerplanar} if it has a drawing in which every vertex lies on the boundary of the outer face. 
Show that a graph is outerplanar if and only if it contains neither $K^4$ nor $K_{2,3}$ as a minor.}

\cleardoublepage

% Question 5
\question{5}{Prove or disprove: Every planar bipartite graph has a vertex of degree at most 3.}

\cleardoublepage

% Question 6
\question{6}{Show that the complement of any planar graph with 11 or more vertices is not planar. (It has been shown that the above statement is true 
when 11 is replaced by 9, and there are examples of planar graphs with 8 vertices having planar complement.)}

\end{document}
