Practice Definition Of Hamiltonian Circuit And Hamiltonian Path (2.1.1)

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6 sample questions

Question 1.
Define Hamiltonian Circuit.
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Think about a loop that goes around a graph.
Question 2.
What is a Hamiltonian Path?
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Consider it like a tour that doesn't have to loop back.
3Question 3.
What constitutes a Hamiltonian circuit?
- Visits all edges
- Visits all vertices exactly once
- Can repeat vertices
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Focus on the vertex requirement.
4Question 4.
True or False: An Euler circuit can also be a Hamiltonian circuit.
- True
- False
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Think about what each circuit focuses on.
Question 5.
Given a graph with a vertex degree distribution, prove whether it satisfies Dirac's or Ore's theorem or neither.
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Compare degree sums and adjacency pairs carefully.
Question 6.
Create your own small graph and identify Hamiltonian circuits or paths within it.
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Use graphical tools or drawings for clarity.

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