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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 criteria for visiting vertices in a closed loop.
Question 2
Easy
What is Ore's condition in relation to Hamiltonian graphs?
💡 Hint: Consider the role of vertex degrees in forming connections.
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?
- A circuit that visits each vertex once
- A circuit that visits some vertices
- A circuit that can revisit vertices
💡 Hint: A Hamiltonian tour avoids repetition.
Question 2
True or False: Ore's condition must always guarantee a Hamiltonian cycle.
- True
- False
💡 Hint: Consider graphs that satisfy Ore's condition without forming cycles.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Analyze a graph with vertices A, B, C, D, E arranged such that A-B, A-C, C-D, D-E are edges. Determine if Ore's condition holds and justify your conclusion.
💡 Hint: Be methodical in your degree counts and remember the basics of degree sums.
Question 2
Design a minimal graph of 7 characters where Ore's condition is satisfied, but the graph is not Hamiltonian. Explain your configuration.
💡 Hint: Focus on distributing vertex connections strategically.
Challenge and get performance evaluation