Practice Hamiltonian Circuit (2.1) - Hamiltonian Circuit - Discrete Mathematics

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6 sample questions

Question 1.
Define Hamiltonian circuit in your own words.
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Think of a tour where you return to the start.
Question 2.
What is the key difference between Hamiltonian and Eulerian circuits?
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Consider what each path emphasizes.
3Question 3.
What is a Hamiltonian Circuit?
- Visits every edge
- Visits every vertex exactly once
- Starts and ends at different points
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Compare with Euler circuits.
4Question 4.
True or False: Ore’s theorem can guarantee a Hamiltonian graph for all configurations.
- True
- False
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Consider if other conditions exist.
Question 5.
Create a graph of 6 vertices that fails both Dirac's and Ore's conditions but is still Hamiltonian.
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Think of how to strategically place vertices for limited connections.
Question 6.
Using Ore's theorem, illustrate how to modify a graph to ensure it meets Hamiltonian conditions.
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Identify pairs and keep track of their degree counts.

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