4.6 - Question 5
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Practice Questions
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What is the vertex chromatic number?
💡 Hint: Think of a scenario where you need to color a map.
Consider two graphs F and H with chromatic numbers of 3 and 4, respectively. What can you conclude about the chromatic number of their union graph G?
💡 Hint: Reflect on the concepts of overlapping colors when vertices are united.
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Interactive Quizzes
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What is the vertex chromatic number of a complete graph with 5 vertices?
💡 Hint: Consider the total number of vertices.
True or False: The chromatic number of the union of two graphs is always equal to the sum of their individual chromatic numbers.
💡 Hint: Think about how colors might overlap.
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Challenge Problems
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Given two graphs, one with a chromatic number of 2 and another with a chromatic number of 5, explore the possible chromatic numbers of their union and explain your reasoning.
💡 Hint: Reflect upon overlapping edges and colors as members join.
Create a complete bipartite graph and a disconnected graph, calculate their chromatic numbers, and analyze their union chromatic number.
💡 Hint: Visualize both graphs and imagine their union.
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