Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a bipartite graph?
💡 Hint: Think about how the vertices can be split.
Question 2
Easy
Define Hall's Marriage Theorem in simple terms.
💡 Hint: Focus on the terms 'matching' and 'condition'.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is required for a complete matching to exist according to Hall's theorem?
- |N(A)| < |A|
- |N(A)| = |A|
- |N(A)| ≥ |A|
💡 Hint: Remember the conditions that must hold.
Question 2
True or False: A bipartite graph cannot have a complete matching if any subset has fewer neighbours than its size.
- True
- False
💡 Hint: Think about Hall's necessary condition.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Construct a bipartite graph with 5 nodes in V1 and 6 in V2, and illustrate a case where Hall's condition does not hold true.
💡 Hint: Make sure to check subsets carefully.
Question 2
Prove that a complete matching exists in a bipartite graph where every student is guaranteed to have at least 2 job offers.
💡 Hint: Think about matching strategies.
Challenge and get performance evaluation