Practice Vertex Colouring Problem (3.1.2) - Vertex and Edge Colouring - Discrete Mathematics

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6 sample questions

Question 1.
What is the vertex colouring problem?
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Think of scheduling conflicts.
Question 2.
Define chromatic number.
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Remember how you schedule your subjects!
3Question 3.
What does vertex coloring aim to achieve?
- Two adjacent vertices have the same color
- No two adjacent vertices share the same color
- Using as many colors as possible
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Relate it back to exam scheduling.
4Question 4.
True or False: The chromatic number can be determined efficiently for all types of graphs.
- True
- False
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Remember the challenges with large graphs.
Question 5.
Create a graph with 5 vertices and describe how many colors you can use at minimum for a valid coloring. Justify your reasoning.
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Draw different combinations to find a minimal color scheme.
Question 6.
Using a graph of your choice, implement the greedy algorithm step-by-step to show the coloring process and explain the results. Discuss if the coloring is optimal.
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Visual aids can assist in understanding the algorithm's application.

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