Unformatted text preview: you started? (b) If you do a walk on K n , on average, how many stepss does it take until you have visited every vertex at least once? (c) Find a simple, directed graph with 15 vertices, one picked as the starting vertex, so that on average it will take more than 5000 steps to get back to the start. 4. Connectivity Detective You are a detective hired to investigate an simple, undirected graph. You have a list of all n vertices. There are two special vertices s and t . You need to ﬁnd out if there is a path from s to t . You start oﬀ knowing nothing about the edges. The only questions you can ask is if there is an edge between two vertices. How many questions do you need to answer for certain whether there is a path from s to t ? Prove that your answer is optimal....
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 Summer '08
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 Math

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