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6.1. Question 10: Edge Colouring in Graphs

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  1. 1.

    What is edge colouring?

    Hint

    Think about how edges interact in a graph.

  2. 2.

    How many edges can you colour with one colour if n is even?

    Hint

    Consider the relationship between vertices and edges.

  3. 3.

    What is the maximum number of edges that can be coloured with the same colour in an even vertex graph?

    • n
    • n/2 + 1
    • n - 1
    Hint

    Remember how the count of edges relates to vertices.

  4. 4.

    Is it possible to colour an odd vertex graph with fewer than n colours?

    • True
    • False
    Hint

    Consider how edges would conflict.

  5. 5.

    Given a complete graph with 9 vertices, calculate the minimum number of colours needed for a proper edge colouring and justify your reasoning.

    Hint

    Visualize how edges conflict with one another.

  6. 6.

    Create a colour assignment for a complete graph with 6 vertices, ensuring all edges are coloured distinctly. Provide a visual representation.

    Hint

    Draw it out to see the conflicts.

Exercises

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Quiz

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting

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Challenge Problems

Total Questions

2

Estimated Time

4 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting