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# worksheet2 - MA 1002 Worksheet 2 Due Date Print Name...

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MA 1002 Worksheet 2 Due Date: September 24, 2009 Print Name: Signature: ID #: Instructor/Section: Instructions: Explain each step using the conventions from class. Please mark solutions clearly. You will not receive full credit for a correct answer without explanation. 1. (25 points) Give an example of a graph that has (a) A Hamiltonian cycle but no Eulerian cycle (b) A Eulerian cycle but no Hamiltonian cycle. 2. (25 points) Definition: An Euler trail is a walk (not necessarily closed) which traverses every edge in a graph exactly once. blue red The northern bank of the river is occupied by the Schloß, or castle, of the Blue Prince; the southern by that of the Red Prince. The east bank is home to the 1

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Bishop’s Kirche, or church; and on the small island in the center is a Gasthaus, or inn. (a) In the representation of K¨onigsberg above, the blue prince, having analyzed the town’s bridge system by means of graph theory, concludes that the bridges cannot be walked. He contrives a stealthy plan to build an eighth bridge so
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worksheet2 - MA 1002 Worksheet 2 Due Date Print Name...

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