Practice Critical Pair Of Vertices And Conclusion (2.1.5)

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6 sample questions

Question 1.
Define a Hamiltonian circuit.
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Think about the properties of simple circuits.
Question 2.
What defines a Hamiltonian path?
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Focus on the difference from circuits.
3Question 3.
Which of the following defines a Hamiltonian circuit?
- Visits every vertex at least once
- Visits every edge at least once
- Visits every vertex exactly once and returns to the starting vertex
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Focus on the goal of the circuit.
4Question 4.
True or False: A Hamiltonian graph must always satisfy Dirac's theorem.
- True
- False
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Consider examples that challenge the theorem.
Question 5.
Given a complete graph with n vertices, prove it is Hamiltonian using Dirac's theorem.
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Consider the definition of complete graphs.
Question 6.
Construct examples of graphs that do not satisfy Ore's condition but are still Hamiltonian and explain your findings.
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Think about different structures that still connect all vertices.

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