Enrol to start learning
Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.
3.2.3. Lower and Upper Bound on Edge Chromatic Number
This section
Practice test
10 questions on this section. Wrong answers show you what to read again.
Sign up to take itWhole chapter
Revision test
Mixed questions from across the chapter. Your answers get marked.
Sign up to take itQuick
Flashcard drill
2 cards from this lesson. Good the night before a test.
Try these first
- 1.
What is the edge chromatic number?
Hint
Think about how colors relate to edges.
- 2.
What does Δ(G) represent in graph theory?
Hint
It concerns the highest number of edges connected to a single vertex.
- 3.
What is the edge chromatic number of a complete graph with 3 vertices?
- 1
- 2
- 3
Hint
Visualize the triangle.
- 4.
True or False: The edge chromatic number can exceed Δ(G) + 1.
- True
- False
Hint
Think of the theorem!
- 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.
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
4 more questions available
Enrol freeQuiz
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
Get your answers marked and your progress tracked
Enrol freeChallenge 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