Practice Summary and References - 2.2 | 2. Hamiltonian Circuit | Discrete Mathematics - Vol 3
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Summary and References

2.2 - Summary and References

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a Hamiltonian circuit?

💡 Hint: Think about circuits that don't repeat any vertex.

Question 2 Easy

What is the key difference between a Hamiltonian path and a Hamiltonian circuit?

💡 Hint: Consider whether the end point is the same as the start.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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.

💡 Hint: Think about circuits and their characteristics.

Question 2

Can a graph have a Hamiltonian circuit and not satisfy Dirac's Theorem?

True
False

💡 Hint: Consider what 'sufficient' means in context.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a counterexample of a graph that meets Ore’s condition but lacks a Hamiltonian circuit. Explain why it fails.

💡 Hint: Reflect on vertex connectivity and arrangement.

Challenge 2 Hard

Design a graph that is Hamiltonian, shows Dirac’s theorem being applicable, but not Ore’s theorem. Describe the graphs.

💡 Hint: Examine degree distributions and connectivity.

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Reference links

Supplementary resources to enhance your learning experience.