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sample exam1 - AMS 301 Summer 2009 AMS 301 Sample Exam 1...

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AMS 301, Summer 2009 1 AMS 301 Sample Exam 1 Choose any FIVE of the seven questions. Try to finish them in 55 minutes. 1. True or False. If true, give a short proof. If false, give a counterexample. a) If G is a graph in which all vertices have the same degree, then its complement must also have all vertices of the same degree. b) Every bipartite complete graph K 2,n must be planar. c) Let G be a planar connected graph with every vertex of degree 4, then G has an Euler cycle. 2. Are there 2 graphs isomorphic? Give the isomorphism or explain why none exists. 3. Model the following problem as a graph coloring problem: A banquet center has some different special rooms. Suppose we want to schedule several evening banquets, each of which requires two specific rooms. Banquets that are scheduled on the same evening must use different special rooms. How many evenings are needed to schedule all the banquets without conflicts? a) What exactly does the set of vertices V correspond to?
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