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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 are connected.
Question 2
Easy
Define a complete matching.
💡 Hint: Consider what it means to cover all vertices in one set.
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 does Hall's Marriage Theorem state?
- A matching exists if |N(A)| = |A|
- A matching exists if |N(A)| ≥ |A| for any A
- A matching exists if all vertices are interconnected
💡 Hint: Consider what it means for subsets and their neighbours.
Question 2
True or False: If |N(A)| < |A| for any subset A, a complete matching can exist.
- True
- False
💡 Hint: Think about how many vertices need to be matched.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove Hall’s Marriage Theorem using a specific bipartite graph example and calculating neighbours.
💡 Hint: Draw the bipartite graph and label neighbours.
Question 2
Construct different bipartite graphs, varying the connections, and identify which meet or violate Hall’s conditions.
💡 Hint: Compare neighbour counts with set sizes.
Challenge and get performance evaluation