13.2 Euler Paths and Euler Circuits 863 27. Southeast Asia Cambodia C( ), Laos L( ), Myanmar M( ), Thailand T( ), and Vietnam V( ) a) * b) Yes; T M L V C L T C , , , , , , , c) No Cambodia Thailand Myanmar Laos Vietnam 28. South America Argentina A( ), Bolivia B( ), Brazil Z( ), Chile C( ), Paraguay P( ), and Uruguay U( ) a) * b) Yes; PBZPABCAUZA , , , , , , , , , , c) No Brazil Chile Uruguay Paraguay Bolivia Argentina Locking Doors Recall Joe from Example 5 who runs a gymcleaning service. Joe is also responsible for locking the doors of four other gyms. The floor plans for these gyms are shown in Exercises 29–32. a) Represent each floor plan as a graph. Use the letters shown to label the vertices of the graph and use the letter O to label the vertex that represents the outside of the gym. Place vertex O near where the word Outside is placed in the diagram. b) Determine (state yes or no) whether it is possible for Joe to move through the gym using each doorway of the gym exactly one time. In other words, does an Euler path exist in the graph? c) If your answer to part (b) is yes, determine one such Euler path. 29. Fit 4U A C D E F B Outside a) * b) Yes c) OABCDFCEOA , , , , , , , , , 30. Pop Fitness B Outside A D C E a) * b) Yes c) O E C B A D O , , , , , , (which is also an Euler circuit) 31. Silver’s Gym D E A B C Outside a) * b) No 32. NY Fitness A C B D E Outside a) * b) Yes c) D C A B D E B O E , , , , , , , , Crime Stopper Routes The Greenbriar crime stopper organization (see Example 6) was so successful that the residents shared their strategies with friends living in the subdivisions of Marlow Heights and Temple Hills. The respective maps of these communities are shown in Exercises 33 and 34. a) Determine whether the residents in each subdivision will be able to establish a path through their communities so that each street block is walked exactly one time. b) If yes, where would the residents need to start their walk? *See Instructor Answer Appendix
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