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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a graphic sequence.
💡 Hint: Think about what degree means in relation to graph vertices.
Question 2
Easy
What does the Havel-Hakimi theorem do?
💡 Hint: Recall the theorem's role in validating degree sequences.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a graphic sequence?
- A sequence of colors
- A sequence of integers that shows vertex degrees
- A method for coloring vertices
💡 Hint: Think about how degrees relate to vertex connections.
Question 2
True or False: In an even-numbered vertex graph, more than n/2 edges can share the same color.
- True
- False
💡 Hint: Recall the limitations on connectivity within edge coloring.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation