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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 of a tour that starts and ends at the same vertex.
Question 2
Easy
What does Dirac's theorem specify regarding vertex degrees?
💡 Hint: Recall the minimum degree condition.
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 path visiting all edges
- A path visiting all vertices
- A path visiting some vertices
💡 Hint: Think about what must be visited in a circuit.
Question 2
True or False: Dirac's Theorem is both necessary and sufficient for a graph to be Hamiltonian.
- True
- False
💡 Hint: Consider examples that defy this condition.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Design a graph with 6 vertices that adheres to Ore's condition and prove it is Hamiltonian.
💡 Hint: Start with vertices connected linearly, then add links that do not disrupt the required sums.
Question 2
Prove or disprove Ore's theorem on a bipartite graph by illustrating vertex pairs.
💡 Hint: Consider how bipartite graphs are structured and whether all vertex combinations meet Ore's condition.
Challenge and get performance evaluation