Practice Example Of Non-optimal Colouring (3.1.5) - Vertex and Edge Colouring

Practice: Example of Non-Optimal Colouring

Lesson 3.1.5Vertex and Edge Colouring

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define vertex colouring in your own words.
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Remember how colours relate to adjacency.
Question 2.
What does the chromatic number represent?
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Think about colouring requirements and their limits.
3Question 3.
What does vertex colouring ensure in a graph?
- It ensures adjacent vertices can share the same colour
- It ensures adjacent vertices have different colours
- It ensures less than half the vertices are coloured
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Think about the goal of preventing shared colours among adjacent nodes.
4Question 4.
Is the greedy algorithm guaranteed to produce an optimal colouring?
- True
- False
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Reflect on how the order affects the results.
Question 5.
Given a graph with specific vertices and edges, provide at least two different vertex sequences and demonstrate how each affects the chromatic number.
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Try to visualize the graph and explore various configurations.
Question 6.
Create a graph with a maximum degree of 3 and demonstrate the relationship between its chromatic number and its maximum degree.
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Sketch out different valid colourings to support your finding.

4 more questions in this section. Enroll free to practise them all.