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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.4, Problem 26ES

Textbook Problem

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Animal Housing A researcher has discovered six new species of insects overseas and needs to transport them home. Some species will harm each Other and so cannot be transported in the same container.

Species A cannot be housed with species C or F.

Species B cannot be housed with species D or F.

Species C cannot be housed with species A, D, or E.

Species D cannot be housed with species B, C, or F.

Species E cannot be housed with species C or F.

Species F cannot be housed with species A, B, D, or E.

Draw a graph where each vertex represents a species of insect and an edge Connects two vertices if the species cannot be housed together. Then use graph coloring to determine the minimum number of containers the researcher will need to transport the insects.

To determine

The minimum number of containers that the researcher will need to transport the insects.

**Given:**

Represent the information by a graph

**Calculation:**

Each species is represented by vertex and an edge is connected by two vertices. If the corresponding species cannot be housed each other.

The two species that are connected by an edge cannot be transported in the same container. Suppose a color is correspond to a time slot, then we need to find a coloring for the graph that uses the fewest possible steps for number of colors.The above graph contains circuits with odd number of vertices

Hence the graph is not 2-colorable. Thus the chromatic number for the graph is 3, so there are three different time containers...

Mathematical Excursions (MindTap Course List)

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