CME 305: Discrete Mathematics and Algorithms
Instructor: Professor Amin Saberi ([email protected])
HW#4 – Due 03/19/10
1. A tournament is a complete directed graph i.e. a directed graph which has exactly one
edge between each pair of vertices. A Hamiltonian path is a path that traverses each
vertex exactly once. A random tournament, is a tournament in which the direction of
all edges is selected independently and uniformly at random.
(a) What is the expected value of the number Hamiltonian paths in a random tour
nament?
(b) Use part (
a
) to show that for every n, there is a tournament with
n
players and
at least
n
!
2
n

1
Hamiltonian paths.
2. The Berlin Blockade was one of the ﬁrst major international crises of the Cold War and
the ﬁrst such crisis that resulted in casualties. During the multinational occupation
of postWorld War II Germany, the Soviet Union blocked the Western Allies’ railway
and road access to the sectors of Berlin under their control. Their aim was to force the
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 Winter '09
 Cold War, West Berlin, Hamiltonian Paths, simple greedy algorithm, minimum possible number, number Hamiltonian paths

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