Practice - Case 2: k-sized Subset with Exactly k Neighbours
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
What is a bipartite graph?
💡 Hint: Think about how the vertices can be split.
Define Hall's Marriage Theorem in simple terms.
💡 Hint: Focus on the terms 'matching' and 'condition'.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is required for a complete matching to exist according to Hall's theorem?
💡 Hint: Remember the conditions that must hold.
True or False: A bipartite graph cannot have a complete matching if any subset has fewer neighbours than its size.
💡 Hint: Think about Hall's necessary condition.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.