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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a Hamiltonian circuit?
💡 Hint: Think about circuits that don't repeat any vertex.
Question 2
Easy
What is the key difference between a Hamiltonian path and a Hamiltonian circuit?
💡 Hint: Consider whether the end point is the same as the start.
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 key requirement for a Hamiltonian circuit?
- It must cover all edges of the graph.
- It can repeat vertices.
- It must cover all vertices without repeats.
💡 Hint: Think about circuits and their characteristics.
Question 2
Can a graph have a Hamiltonian circuit and not satisfy Dirac's Theorem?
- True
- False
💡 Hint: Consider what 'sufficient' means in context.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a counterexample of a graph that meets Ore’s condition but lacks a Hamiltonian circuit. Explain why it fails.
💡 Hint: Reflect on vertex connectivity and arrangement.
Question 2
Design a graph that is Hamiltonian, shows Dirac’s theorem being applicable, but not Ore’s theorem. Describe the graphs.
💡 Hint: Examine degree distributions and connectivity.
Challenge and get performance evaluation