Determine how you would solve each of the problems using the techniques: Dijkstra's shortest path algorithm, Euler path, Hamilton cycle, proper vertex coloring, and edge coloring. For each question, describe how you would represent the situation as a graph (state what the edges and vertices are), state the technique you would use, and briefly explain how it answers the given question. You do NOT need to actually solve these problems. Hint: each technique listed above is used exactly once! (a) An airline has flights into and out of many cities; however, this airline only has direct flights between certain pairs of cities, each with a fixed price. You are planning a trip from Chicago to Tokyo, but the airline does not have a direct ight from Chicago to Tokyo. What is the cheapest ight you can book that leaves from Chicago and arrives in Tokyo? (b) Ten members of Math Club are driving to a math conference in a neighboring state. However, some of these students have dated in the past, and things are still a little awkward. Each student lists which other students they refuse to share a car with; these conflicts are recored in the table below. What is the fewest number of cars the club needs to make the trip? Student: A B C D E F G H I J Conflicts: BEJ ADG HJ BF AI DJ B CI EHJ ACFI
Determine how you would solve each of the problems using the techniques: Dijkstra's shortest path
(a) An airline has flights into and out of many cities; however, this airline only has direct flights between certain pairs of cities, each with a fixed price. You are planning a trip from Chicago to Tokyo, but the airline does not have a direct ight from Chicago to Tokyo. What is the cheapest ight you can book that leaves from Chicago and arrives in Tokyo?
(b) Ten members of Math Club are driving to a math conference in a neighboring state.
However, some of these students have dated in the past, and things are still a little awkward. Each student lists which other students they refuse to share a car with; these conflicts are recored in the table below. What is the fewest number of cars the club needs to make the trip?
Student: A B C D E F G H I J
Conflicts: BEJ ADG HJ BF
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