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3.2.3. Lower and Upper Bound on Edge Chromatic Number

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Try these first

  1. 1.

    What is the edge chromatic number?

    Hint

    Think about how colors relate to edges.

  2. 2.

    What does Δ(G) represent in graph theory?

    Hint

    It concerns the highest number of edges connected to a single vertex.

  3. 3.

    What is the edge chromatic number of a complete graph with 3 vertices?

    • 1
    • 2
    • 3
    Hint

    Visualize the triangle.

  4. 4.

    True or False: The edge chromatic number can exceed Δ(G) + 1.

    • True
    • False
    Hint

    Think of the theorem!

  5. 5.

    Design a graph with n vertices where the edge chromatic number is Δ(G) + 1. Justify your construction.

    Hint

    Remember the connectedness of vertices.

  6. 6.

    Given a graph of known maximum degree, propose how you would determine the edge chromatic number in practice, especially with no visual aid.

    Hint

    Consult on practical theoretical approaches.

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