A zoo is going to place its animals in a set of large open areas, instead of hav

Question

A zoo is going to place its animals in a set of large open areas, instead of having animals in individual cages. If two different animals cannot live together peacefully (e.g.. a tiger and deer cannot live together because the tiger will eat the deer), then they must be put in different open areas. The zoo wants to determine the minimum number of open areas needed to safely house all its animals. Model this problem of assigning animals to a minimal number of open areas as a graph coloring problem. What are the vertices, the edges, the colors?

Explanation / Answer

Vertices = Animals

Edges = Animals Can Not Live Together Peeacefully

Colors = Areas Needed to Safely House All Its Animals

Chromatic Numbers = Minimum Number of Open Areas Needed

As we need to assign different animals in open areas, so the vertices will represent the animal type. And as the line joining two vertices will represent the distance between the two animals, so edges will represent that animals can't live together peacefully. After we join the edges, we would color the areas which will be intersection of all the cases. So, Areas needed to safely house all the animals will be represented by the different colors. And finally the chromatin number will represent the minimum number of open areas needed.

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