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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a Hamiltonian circuit.
💡 Hint: Think about the properties of simple circuits.
Question 2
Easy
What defines a Hamiltonian path?
💡 Hint: Focus on the difference from circuits.
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
Which of the following defines a Hamiltonian circuit?
- Visits every vertex at least once
- Visits every edge at least once
- Visits every vertex exactly once and returns to the starting vertex
💡 Hint: Focus on the goal of the circuit.
Question 2
True or False: A Hamiltonian graph must always satisfy Dirac's theorem.
- True
- False
💡 Hint: Consider examples that challenge the theorem.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a complete graph with n vertices, prove it is Hamiltonian using Dirac's theorem.
💡 Hint: Consider the definition of complete graphs.
Question 2
Construct examples of graphs that do not satisfy Ore's condition but are still Hamiltonian and explain your findings.
💡 Hint: Think about different structures that still connect all vertices.
Challenge and get performance evaluation