   # A one-way road intersects a two-way road in a four-way intersection. Each direction has turn lanes and left-turn lights. 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 2EE
Textbook Problem
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## A one-way road intersects a two-way road in a four-way intersection. Each direction has turn lanes and left-turn lights. 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 one-way road intersects a two-way road in a four-way intersection. Each direction has turn lanes and left-turn lights.

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

The possible collisions in each path are:

• A: D, E, G
• B: D, E, F, G
• C: D
• D: A, B, C
• E: A, G, B, F
• F: E, B
• G: A, B, E

In the graph, each vertex represents one of the twelve possible traffic paths and the edge between every two vertices represents the corresponding paths that would allow the vehicles to collide...

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