Ch 5 Notes Part 2

Ch 5 Notes Part 2 - Eulerizations & Semi-Eulerizations...

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Eulerizations Semi-Eulerizations

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Post Office Dept. of Public Works Supermarket Bank Fountain Below is a city map. The edges of the map represent roads. There are houses along each of the roads. Once a week garbage men pick up garbage at each of the houses. They begin their route in the morning at the Dept. of Public Works and return back to the DPW at the end of the day. Can the garbage men service all of the roads without having to re-travel any of the roads?
P D S B You do not need curved lines – it doesn’t make a difference You don’t need to include the fountain as a vertex since it doesn’t have any roads going to it Can the garbage men service all of the roads without having to re-travel any of the roads?

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P D S B Can the garbage men service all of the roads without having to re-travel any of the roads? deg(P) = deg(D) = deg(B) = deg(S) = 3 3 2 2 If the garbage men must start and end at the DPW, it is impossible to service all of the roads without re-traveling any of the roads, since there are odd vertices. An Euler Path is possible, but the garbage men would have to start at the Post Office (or Supermarket) and end at the Supermarket (or Post Office). (No Euler Circuit)
D S B Now the problem is: How do we find a route that requires the least amount of traveling? Time is Money

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This note was uploaded on 05/06/2008 for the course MATH 110 taught by Professor Pietro during the Spring '08 term at SUNY Fredonia.

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Ch 5 Notes Part 2 - Eulerizations & Semi-Eulerizations...

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