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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 a graph.
Question 2
Easy
What is the Havel-Hakimi theorem used for?
💡 Hint: Recall how we prove sequences are graphic.
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 the required edge chromatic number for a complete graph when n is odd?
- n-1
- n
- n+1
💡 Hint: Recall the relationship between edge chromatic numbers and vertex count.
Question 2
True or False: The Havel-Hakimi theorem can be applied to determine graphic sequences.
- True
- False
💡 Hint: Consider the purpose of the theorem.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the sequence [5, 5, 4, 4, 3, 3, 2, 1], prove if it is graphic and present a construction.
💡 Hint: Follow the theorem's steps for reducing the sequence.
Question 2
Calculate the minimum number of colors required for a complete graph of 11 vertices and explain your reasoning.
💡 Hint: Think about how odd numbers affect coloring.
Challenge and get performance evaluation