% Chris Hanusa
% chanusa@qc.cuny.edu	
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\begin{center}\large 
MATH 634, Spring 2014

{\sc Homework 12}

due 5:00{\sc pm} on Wednesday, March 26.
\end{center}

\noindent
%{\em Background reading:} {\em Pearls in Graph Theory}, Section 8.1.
%
%\smallskip\noindent
{\color{red} Follow the posted homework guidelines when completing this assignment.}

\smallskip\noindent
Problems {\bf 12E}, {\bf 12A}, {\bf 12B}, and {\bf 12C},  should be typed (or written up) and handed in as class starts on Wednesday 3/26. 

\begin{enumerate}
\item[\bf 12E.]  Play the planarity game at \url{http://www.planarity.net/}.  Complete levels 1--6 for full credit or levels 1--4 for 3 points out of five.  Complete level 7 for two bonus points.  If possible, email a screen capture of (or print out) the last level you completed with your score and turn it in.

\item[\bf 12A.]
%%13h5,12h4,11h7,14h12
Use an argument involving girth to prove that the Petersen graph is not planar.

\item[\bf 12B.]
%13h5,11h6,14h12
8.1.9abc [In part (c), add edges---do not subtract them.]

\item[\bf 12C.]
%%13h6,14h12
%Pearls 8.1.14
\begin{enumerate}
\item Find a graph $G$ with degree sequence $(4,4,3,3,3,3)$ such that $G$ is planar.   
\item Find a graph $H$ with degree sequence $(4,4,3,3,3,3)$ such that $H$ is non-planar.
\end{enumerate}
Remember to prove that your examples satisfy the given requirements.

\end{enumerate}





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