Practice Vertex Chromatic Number (3.1.3) - Vertex and Edge Colouring - Discrete Mathematics

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6 sample questions

Question 1.
What is the vertex chromatic number?
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Think about how colors can impact adjacency.
Question 2.
Explain the greedy algorithm in simple terms.
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What does 'greedy' imply when choosing colors?
3Question 3.
What does the vertex chromatic number indicate?
- The number of edges
- Minimum colors needed to color vertices
- Maximum degree of a vertex
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Focus on the definition of vertex chromatic number.
4Question 4.
True or False: The greedy algorithm guarantees an optimal vertex coloring solution.
- True
- False
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Consider examples where coloring can differ.
Question 5.
Given a graph with 6 vertices and edges connecting them in a way that forms a cycle, calculate its chromatic number and explain your reasoning.
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Count the edges and see how they connect!
Question 6.
Design a scenario in which a greedy algorithm fails to find the optimal solution in vertex coloring, detailing your graph structure.
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Imagine selecting corners of triangles one by one and how color constraints apply.

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