Practice Summary And References (2.2) - Hamiltonian Circuit - Discrete Mathematics

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6 sample questions

Question 1.
What is a Hamiltonian circuit?
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Think about circuits that don't repeat any vertex.
Question 2.
What is the key difference between a Hamiltonian path and a Hamiltonian circuit?
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Consider whether the end point is the same as the start.
3Question 3.
What is a key requirement for a Hamiltonian circuit?
- It must cover all edges of the graph.
- It can repeat vertices.
- It must cover all vertices without repeats.
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Think about circuits and their characteristics.
4Question 4.
Can a graph have a Hamiltonian circuit and not satisfy Dirac's Theorem?
- True
- False
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Consider what 'sufficient' means in context.
Question 5.
Given a counterexample of a graph that meets Ore’s condition but lacks a Hamiltonian circuit. Explain why it fails.
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Reflect on vertex connectivity and arrangement.
Question 6.
Design a graph that is Hamiltonian, shows Dirac’s theorem being applicable, but not Ore’s theorem. Describe the graphs.
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Examine degree distributions and connectivity.

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