Practice Critical Pair of Vertices and Conclusion - 2.1.5 | 2. Hamiltonian Circuit | Discrete Mathematics - Vol 3
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Critical Pair of Vertices and Conclusion

2.1.5 - Critical Pair of Vertices and Conclusion

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a Hamiltonian circuit.

💡 Hint: Think about the properties of simple circuits.

Question 2 Easy

What defines a Hamiltonian path?

💡 Hint: Focus on the difference from circuits.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Focus on the goal of the circuit.

Question 2

True or False: A Hamiltonian graph must always satisfy Dirac's theorem.

True
False

💡 Hint: Consider examples that challenge the theorem.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a complete graph with n vertices, prove it is Hamiltonian using Dirac's theorem.

💡 Hint: Consider the definition of complete graphs.

Challenge 2 Hard

Construct examples of graphs that do not satisfy Ore's condition but are still Hamiltonian and explain your findings.

💡 Hint: Think about different structures that still connect all vertices.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.