Air Travel and Euler
The maps that pilots use are called route maps. Route maps show the paths of the airplanes from one destination to another. Here is an example of an actual route map from Frontier Airlines. The center for all travel with this airline is in Denver, Colorado. From there you can travel to some of the major cities in the surrounding states.
Can you decide whether the above route map is a circuit, path or neither?

Below is another route map. This map is used by Reno Air which is based in Reno, Nevada. The graph that is made from the destinations (vertices) and the connections made among the desitnations (arcs) is a bit more complex than the graph from Frontier Airlines. There are many more cities as well as ways to get from one city to the next.
To analyze the above network, it might be easiest to redraw the graph
so that the cities are more spread out.
Now can you tell if this map is a circuit or a path, or is it neither?

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