Practice Edge Colouring (3.2) - Vertex and Edge Colouring - Discrete Mathematics

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6 sample questions

Question 1.
What is edge colouring?
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Think about how colours differ in a graph.
Question 2.
What does the edge chromatic number denote?
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Consider the minimum colours necessary to avoid conflicts.
3Question 3.
What is the purpose of edge colouring in graph theory?
- To assign colours to vertices
- To assign colours to edges
- To create a complete graph
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Think about what graph components we are colouring.
4Question 4.
True or False: The maximum degree of a vertex gives a lower bound for edge chromatic number.
- True
- False
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Remember how edges are connected to vertices.
Question 5.
For a graph consisting of 8 nodes with varying degrees, demonstrate the edge colouring process while illustrating the chromatic number.
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Keep track of which colours you've assigned.
Question 6.
Design a scheduling algorithm for a tournament with 10 teams, ensuring no two matches occur on the same day for any team. Calculate the edge chromatic number.
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Draw the graph and assign colours carefully, counting distinct colours used.

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