2.2 - Summary and References
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Practice Questions
Test your understanding with targeted questions
What is a Hamiltonian circuit?
💡 Hint: Think about circuits that don't repeat any vertex.
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.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a key requirement for a Hamiltonian circuit?
💡 Hint: Think about circuits and their characteristics.
Can a graph have a Hamiltonian circuit and not satisfy Dirac's Theorem?
💡 Hint: Consider what 'sufficient' means in context.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
Supplementary resources to enhance your learning experience.