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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define Hamiltonian circuit in your own words.
💡 Hint: Think of a tour where you return to the start.
Question 2
Easy
What is the key difference between Hamiltonian and Eulerian circuits?
💡 Hint: Consider what each path emphasizes.
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 Hamiltonian Circuit?
- Visits every edge
- Visits every vertex exactly once
- Starts and ends at different points
💡 Hint: Compare with Euler circuits.
Question 2
True or False: Ore’s theorem can guarantee a Hamiltonian graph for all configurations.
- True
- False
💡 Hint: Consider if other conditions exist.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Create a graph of 6 vertices that fails both Dirac's and Ore's conditions but is still Hamiltonian.
💡 Hint: Think of how to strategically place vertices for limited connections.
Question 2
Using Ore's theorem, illustrate how to modify a graph to ensure it meets Hamiltonian conditions.
💡 Hint: Identify pairs and keep track of their degree counts.
Challenge and get performance evaluation