2.1.3 - Ore's Condition
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Practice Questions
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Define a Hamiltonian circuit.
💡 Hint: Think about the criteria for visiting vertices in a closed loop.
What is Ore's condition in relation to Hamiltonian graphs?
💡 Hint: Consider the role of vertex degrees in forming connections.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a Hamiltonian circuit?
💡 Hint: A Hamiltonian tour avoids repetition.
True or False: Ore's condition must always guarantee a Hamiltonian cycle.
💡 Hint: Consider graphs that satisfy Ore's condition without forming cycles.
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Challenge Problems
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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.
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.
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