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392
Solutions to Exercises
(b) After the first night, we remove the edges corresponding to the dates which occurred. We are left
with a bipartite graph in which every vertex has degree 4. Again, Problem 6 guarantees a perfect
matching. Continue for the five nights, reducing the degree by 1 each time.
6. (a) [BB] Bruce
+t
Maurice, Edgar
+t
Michael, Eric
+t
Roland, Herb
+t
Richard.
(b)
If
Roland and Bruce share a canoe, then Maurice and Michael would both have to be with Edgar.
(c) No.
If
Bruce and Roland were together, then both Maurice and Michael would have to be in the
same canoe with Edgar. On the other hand, if Bruce and Roland were not in the same canoe, then
Bruce and Roland would have to be in the same canoe with Maurice and Michael (in some order),
leaving no one for Edgar since he refuses to be with Herb.
7. (a) [BB] Construct a bipartite graph with vertex sets VI and
V2,
where VI has
n
vertices corresponding
to
AI,
... ,
An, V2
has one vertex for each element of
S
and there is an edge joining
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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