   # A two-way road intersects another two-way road in a four-way intersection. One road has left turn lanes with left-turn lights, but on the other road cars are not allowed to make left turns. Represent the various traffic routes with a graph and use graph coloring to determine the minimum number of stages required for a light cycle. Then refine your design to allow as much traffic as possible to proceed at each stage Of the cycle. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.4, Problem 3EE
Textbook Problem
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## A two-way road intersects another two-way road in a four-way intersection. One road has left turn lanes with left-turn lights, but on the other road cars are not allowed to make left turns. Represent the various traffic routes with a graph and use graph coloring to determine the minimum number of stages required for a light cycle. Then refine your design to allow as much traffic as possible to proceed at each stage Of the cycle.

To determine

The minimum number of stages required for a light cycle using graph colouring.

### Explanation of Solution

Given information:

A two-way road intersects another two-way road in a four-way intersection. One road has left-turn lanes with left-turn lights, but on the other road cars are not allowed to make left turns.

By the given information, the possible routes are given in the following diagram.

The possible collisions in each path are:

• A: D, J, I, E, H
• B: D
• C: G, J
• D: G, J, A, B
• E: G, J, I, A, H
• F: I
• G: I, E, D, C, J
• H: E, A
• I: A, E, G, F
• J: A, E, D, C, G

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