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\begin{flushleft}
          Fall 93\\
          Math 475 \\
          A.Miller
\end{flushleft}

\vspace{.5in}

       Due  Mon Dec 13

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  Chapter 11  p. 482-490

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\centerline{ 5 20 21 28 30 41 44 49 53 56}

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 Chapter 12  p. 540-542

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\centerline{4 5 19}

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(A) Prove Theorem 11.8.2 page 474.

(B) Suppose $G=(V,E)$ is a graph with the property that
deg$(v)\geq k$ for every $v\in V$.  Prove that $G$ has a path
with at least $k+1$ distinct vertices on it.

(C) Suppose twelve people are at a dinner party in which every
person knows at least six others. Prove that all twelve can be
seated at a circular table in such a way that each person is
acquanted with the persons sitting on either side.

(D) Show that if one edge is removed from the graph $K_5$ the resulting
graph is planar.  Is the same thing true for $K_{3,3}$?


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\begin{center}
{\Large \bf Final Exam:\\
 Monday, Dec 20, 12:25-2:25\\
 434 Education.}
\end{center}

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