2.1.4 - Proof of Ore's Theorem
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Practice Questions
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Define a Hamiltonian circuit.
💡 Hint: Think of a tour that starts and ends at the same vertex.
What does Dirac's theorem specify regarding vertex degrees?
💡 Hint: Recall the minimum degree condition.
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Interactive Quizzes
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What is a Hamiltonian circuit?
💡 Hint: Think about what must be visited in a circuit.
True or False: Dirac's Theorem is both necessary and sufficient for a graph to be Hamiltonian.
💡 Hint: Consider examples that defy this condition.
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Challenge Problems
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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.
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.
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