Practice Ore's Condition (2.1.3) - Hamiltonian Circuit - Discrete Mathematics - Vol 3

Practice: Ore's Condition

Lesson 2.1.3Hamiltonian Circuit

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10 questions

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6 sample questions

Question 1.
Define a Hamiltonian circuit.
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Think about the criteria for visiting vertices in a closed loop.
Question 2.
What is Ore's condition in relation to Hamiltonian graphs?
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Consider the role of vertex degrees in forming connections.
3Question 3.
What is a Hamiltonian circuit?
- A circuit that visits each vertex once
- A circuit that visits some vertices
- A circuit that can revisit vertices
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A Hamiltonian tour avoids repetition.
4Question 4.
True or False: Ore's condition must always guarantee a Hamiltonian cycle.
- True
- False
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Consider graphs that satisfy Ore's condition without forming cycles.
Question 5.
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.
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Be methodical in your degree counts and remember the basics of degree sums.
Question 6.
Design a minimal graph of 7 characters where Ore's condition is satisfied, but the graph is not Hamiltonian. Explain your configuration.
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Focus on distributing vertex connections strategically.

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