3012 Final Exam

3012 Final Exam - Su09: MATH 3012 Applied Combinatorics...

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Unformatted text preview: Su09: MATH 3012 Applied Combinatorics Carl Yerger Tuesday 7/28/2009 Final Exam 170 minutes Name: Student ID: Instructions. 1. Attempt all questions. 2. The questions on this test sum to 305 points, but the test will be scored out of 300 points. 3. Show all the steps of your work clearly. Use complete sentences. Points may be deducted for lack of clarity or poor mathematical exposition. Neatness counts! 4. Calculators are not permitted on this exam nor the use of any other electronic devices. 5. No collaboration of any kind is permitted on this exam. 6. As a reminder, the Georgia Tech Honor Code applies to all matters of conduct in this course. Question Points Your Score Q1 75 Q2 15 Q3 15 Q4 20 Q5 30 Q6 20 Q7 20 Q8 15 Q9 25 Q10 30 Q11 20 Q12 20 TOTAL 300 1. [75 points total, 5 points each part] a. State Eulers formula for planar graphs. b. Suppose G is a graph with 100 vertices and 300 edges. Could G be planar? Explain your answer. c. What are the partitions of 7? d. What is the generating function for the number of partitions of square numbers? e. What does Diracs theorem say about Hamiltonian graphs? f. Suppose I have a graph with 40 vertices and 600 edges. Must there exist a Hamiltonian cycle in thisSuppose I have a graph with 40 vertices and 600 edges....
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3012 Final Exam - Su09: MATH 3012 Applied Combinatorics...

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