Practice Edge Chromatic Number (3.2.2) - Vertex and Edge Colouring - Discrete Mathematics

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6 sample questions

Question 1.
What is the edge chromatic number of a graph?
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Think about how edges are related to vertices.
Question 2.
Define maximum degree (Δ(G)).
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Consider the most connected vertex in the graph.
3Question 3.
What does the edge chromatic number of a graph refer to?
- The number of colors needed for vertices
- The number of colors needed for edges
- The maximum degree of the graph
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Focus on what is being colored; edges or vertices.
4Question 4.
True or False: The edge chromatic number can be less than the maximum degree of a vertex.
- True
- False
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Think about the implications of adjacent edges.
Question 5.
Given a pentagon graph (5 vertices forming a cycle), what is the edge chromatic number? Prove your answer.
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Draw the graph and try applying colors to the edges.
Question 6.
Create a scenario with a bipartite graph and evaluate its edge chromatic number.
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Bipartite graphs have special properties related to colors.

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