Practice Lower And Upper Bound On Edge Chromatic Number (3.2.3)

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6 sample questions

Question 1.
What is the edge chromatic number?
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Think about how colors relate to edges.
Question 2.
What does Δ(G) represent in graph theory?
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It concerns the highest number of edges connected to a single vertex.
3Question 3.
What is the edge chromatic number of a complete graph with 3 vertices?
- 1
- 2
- 3
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Visualize the triangle.
4Question 4.
True or False: The edge chromatic number can exceed Δ(G) + 1.
- True
- False
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Think of the theorem!
Question 5.
Design a graph with n vertices where the edge chromatic number is Δ(G) + 1. Justify your construction.
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Remember the connectedness of vertices.
Question 6.
Given a graph of known maximum degree, propose how you would determine the edge chromatic number in practice, especially with no visual aid.
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Consult on practical theoretical approaches.

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