Practice Vertex Colouring Motivation (3.1.1)

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6 sample questions

Question 1.
Define vertex colouring in the context of graph theory.
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Think about adjacent vertices.
Question 2.
What does the vertex chromatic number represent?
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Consider what the minimum means.
3Question 3.
What is vertex colouring?
- Assigning colors to edges in a graph
- The process of assigning colors to vertices in a graph
- The number of colors in a graph
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Think about where colors are assigned.
4Question 4.
True or False: The vertex chromatic number is always equal to the number of vertices in the graph.
- True
- False
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Consider when you might need fewer colors.
Question 5.
Given a graph with 12 vertices and a maximum degree of 6, create a set of vertex color assignments that achieves optimal colouring for a scheduling scenario.
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Start from the highest degree vertices down.
Question 6.
Demonstrate a scenario in which the greedy coloring algorithm fails to produce an optimal number of colors. Construct a small graph example for clarity.
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Think about conflicting edges.

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