Practice Legal Coloring Of Graphs (18.2.6) - Design and Analysis of Algorithms

Practice: Legal Coloring of Graphs

Lesson 18.2.6Design and Analysis of Algorithms

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8 questions

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6 sample questions

Question 1.
What is a graph?
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Think about how points and connections relate.
Question 2.
What must be true for two adjacent vertices in a colored graph?
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Consider the purpose of distinguishing points.
3Question 3.
What is the main goal of graph coloring?
- To assign colors randomly
- To ensure no adjacent vertices share the same color
- To create decorative maps
- To analyze map sizes
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Think about the purpose of making distinctions between adjacent regions.
4Question 4.
True or False: The four color theorem states that at least four colors are needed for any planar map.
- True
- False
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Revisit what the theorem's assertion is regarding color necessity.
Question 5.
Create a graph of a fictional country with at least 10 states, ensuring no two neighboring states share the same color. Present your graph and explain your coloring strategy.
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Start by mapping out the connections before coloring.
Question 6.
Examine a complex map that uses more than four colors. Discuss how the four color theorem applies despite the use of additional colors for effective distinctions.
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Think about artistic intent versus mathematical requirements.

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