Practice Question 12: Greedy Strategy For Vertex Colouring (6.3) - Question 9: Proving a Graphic Sequence

Practice: Question 12: Greedy Strategy for Vertex Colouring

Lesson 6.3Question 9: Proving a Graphic Sequence

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8 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define vertex colouring.
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Think about the application in scheduling.
Question 2.
What does the Welsh-Powell algorithm do?
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3Question 3.
What does the Welsh-Powell algorithm follow?
- Sorting vertices by alphabet
- Sorting vertices by degree
- Randomly selecting vertices
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Focus on the concept of degrees.
4Question 4.
True or False: The Welsh-Powell algorithm always finds the optimal solution for vertex colouring.
- True
- False
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Think about the scenarios we've discussed.
Question 5.
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.
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Start with the vertex that has the highest degree.
Question 6.
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.
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Challenge yourself: consider how to minimize colours based on vertex connections.

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