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\title{General Mathematics and Computational Science II}
\author{Exercise 11}
\date{March 20, 2007}
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\begin{enumerate}

\item Write out the proof that (3) implies (4) in Ivanov, p.\ 90,
Theorem 3.

\item Ivanov, p. 92, Exercise:  Generalize Euler's formula to the case
of an arbitrary (i.e., not necessarily connected) planar graph.

\item Ivanov, p. 92, Exercise: Prove that the complete graph of 5
vertices (i.e., with every vertex adjacent to every other) cannot be
embedded in the plane.

\end{enumerate}
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