Practice Vertex And Edge Colouring (3) - Vertex and Edge Colouring - Discrete Mathematics

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6 sample questions

Question 1.
Define vertex colouring.
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Think about scheduling.
Question 2.
What is the goal of edge colouring?
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Consider tournament matches.
3Question 3.
What is the vertex chromatic number?
- The number of edges in a graph
- The minimum number of colours needed to colour a graph
- The maximum degree of a vertex
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Think about preventing colour conflicts.
4Question 4.
True or False: The greedy algorithm guarantees an optimal solution for vertex colouring.
- True
- False
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Consider the order in which you pick vertices.
Question 5.
Given a complex graph with multiple vertices and edges, use the greedy algorithm to determine the chromatic number. Discuss whether the result is optimal.
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Draw the graph and apply the algorithm step-by-step.
Question 6.
Design a simple graph and explain how you would schedule a round-robin tournament using edge colouring. Calculate the edge chromatic number using the Gupta-Vizing theorem.
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Visualize the tournament as a complete graph.

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