6.2.1 - Case When n is Even
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Practice Questions
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Define a graphic sequence.
💡 Hint: Think about what degree means in relation to graph vertices.
What does the Havel-Hakimi theorem do?
💡 Hint: Recall the theorem's role in validating degree sequences.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a graphic sequence?
💡 Hint: Think about how degrees relate to vertex connections.
True or False: In an even-numbered vertex graph, more than n/2 edges can share the same color.
💡 Hint: Recall the limitations on connectivity within edge coloring.
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Challenge Problems
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Given a sequence of degrees (4, 3, 3, 1), can this represent a graphic sequence? If so, construct the graph. If not, explain why.
💡 Hint: Start with the highest degree and connect accordingly while verifying at each step.
You have a complete graph of 10 vertices. How can you schedule a round-robin tournament such that no team plays more than once per day? Describe your coloring scheme.
💡 Hint: Think about rotation based on positions to avoid repeating encounters.
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