Chapter 14.2, Problem 48E

In Exercises 45-48, we revisit the four-block, neighborhood discussed in the previous section. Recall that a mail carrier parks her truck at the intersection shown in the figure and then walks to deliver mail to each of the houses. The streets on the outside of the neighborhood have houses on one side only. The interior streets have houses on both sides of the street. On these streets, the mail carrier must walk down the street twice, covering each side of the street separately. A graph that models the streets of the neighborhood walked by the mail carrier is shown.

A security guard needs to walk the streets of the neighborhood. Unlike the postal worker, the guard is to walk down each street once, whether or not the street has houses on both sides. Draw a graph that models the streets of the neighborhood walked by the security guard. Then determine whether the residents in the neighborhood will be able to establish a route for the security guard so that each street is walked exactly once. If this is possible, use your map to show where the guard should begin the walk.