3.1.5 - Example of Non-Optimal Colouring
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Practice Questions
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Define vertex colouring in your own words.
💡 Hint: Remember how colours relate to adjacency.
What does the chromatic number represent?
💡 Hint: Think about colouring requirements and their limits.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does vertex colouring ensure in a graph?
💡 Hint: Think about the goal of preventing shared colours among adjacent nodes.
Is the greedy algorithm guaranteed to produce an optimal colouring?
💡 Hint: Reflect on how the order affects the results.
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Challenge Problems
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Given a graph with specific vertices and edges, provide at least two different vertex sequences and demonstrate how each affects the chromatic number.
💡 Hint: Try to visualize the graph and explore various configurations.
Create a graph with a maximum degree of 3 and demonstrate the relationship between its chromatic number and its maximum degree.
💡 Hint: Sketch out different valid colourings to support your finding.
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