Practice Question 12: Greedy Strategy for Vertex Colouring - 6.3 | 6. Question 9: Proving a Graphic Sequence | Discrete Mathematics - Vol 3
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6.3 - Question 12: Greedy Strategy for Vertex Colouring

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define vertex colouring.

💡 Hint: Think about the application in scheduling.

Question 2

Easy

What does the Welsh-Powell algorithm do?

💡 Hint: No hint provided

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does the Welsh-Powell algorithm follow?

  • Sorting vertices by alphabet
  • Sorting vertices by degree
  • Randomly selecting vertices

💡 Hint: Focus on the concept of degrees.

Question 2

True or False: The Welsh-Powell algorithm always finds the optimal solution for vertex colouring.

  • True
  • False

💡 Hint: Think about the scenarios we've discussed.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a graph with 6 vertices in a cycle, apply the Welsh-Powell algorithm and determine if it results in using more colours than optimal.

💡 Hint: Start with the vertex that has the highest degree.

Question 2

Create a more complex graph with connections among vertices, illustrating where the Welsh-Powell algorithm may fail to be optimal. Then show the optimal colour assignment.

💡 Hint: Challenge yourself: consider how to minimize colours based on vertex connections.

Challenge and get performance evaluation