hw4 - CME 305: Discrete Mathematics and Algorithms...

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CME 305: Discrete Mathematics and Algorithms Instructor: Professor Amin Saberi (saberi@stanford.edu) 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 post-World 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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hw4 - CME 305: Discrete Mathematics and Algorithms...

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