3.1.6 - Upper Bound on Vertex Chromatic Number
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Practice Questions
Test your understanding with targeted questions
What does vertex coloring involve?
💡 Hint: Think about graph connections.
What is the maximum degree Δ(G)?
💡 Hint: Consider the vertex with the most connections.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the vertex chromatic number of a graph?
💡 Hint: Focus on the definition of chromatic number.
True or False: The greedy algorithm can always give the optimal coloring.
💡 Hint: Consider how order affects the results.
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Challenge Problems
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Consider a graph of 6 vertices forming a cycle. Determine the chromatic number and explain your reasoning.
💡 Hint: Visualize the sequence of colors placed around the cycle.
Design a graph that can be colored optimally with 3 colors yet a greedy algorithm may suggest 4, and explain.
💡 Hint: Investigate the edges connecting two groups.
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