Practice Upper Bound On Vertex Chromatic Number (3.1.6)

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6 sample questions

Question 1.
What does vertex coloring involve?
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Think about graph connections.
Question 2.
What is the maximum degree Δ(G)?
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Consider the vertex with the most connections.
3Question 3.
What is the vertex chromatic number of a graph?
- The maximum number of edges
- The minimum number of colors needed for coloring
- The average of the degrees
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Focus on the definition of chromatic number.
4Question 4.
True or False: The greedy algorithm can always give the optimal coloring.
- True
- False
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Consider how order affects the results.
Question 5.
Consider a graph of 6 vertices forming a cycle. Determine the chromatic number and explain your reasoning.
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Visualize the sequence of colors placed around the cycle.
Question 6.
Design a graph that can be colored optimally with 3 colors yet a greedy algorithm may suggest 4, and explain.
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Investigate the edges connecting two groups.

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