Practice Example of Non-Optimal Colouring - 3.1.5 | 3. Vertex and Edge Colouring | Discrete Mathematics - Vol 3
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Example of Non-Optimal Colouring

3.1.5 - Example of Non-Optimal Colouring

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define vertex colouring in your own words.

💡 Hint: Remember how colours relate to adjacency.

Question 2 Easy

What does the chromatic number represent?

💡 Hint: Think about colouring requirements and their limits.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Think about the goal of preventing shared colours among adjacent nodes.

Question 2

Is the greedy algorithm guaranteed to produce an optimal colouring?

True
False

💡 Hint: Reflect on how the order affects the results.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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Reference links

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