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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is Hall's Marriage Theorem?
💡 Hint: Think about pairs and their connections in a graph.
Question 2
Easy
Define a bipartite graph.
💡 Hint: Consider how edges connect different groups.
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 assert?
- A complete matching exists if |N(A)| ≥ |A| for subsets A.
- A complete matching is impossible.
- Every element in V1 must be connected to V2.
💡 Hint: Think about matching connections.
Question 2
True or False: The sufficient condition is about having a complete matching.
- True
- False
💡 Hint: Recall the theorem's implications.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Provided a bipartite graph, demonstrate the failure of the matching condition. What modifications would result in a valid matching?
💡 Hint: Analyze subsets closely.
Question 2
Construct a complex bipartite graph with 8 and 7 vertices. Illustrate using Hall's theorem whether a complete matching exists.
💡 Hint: Focus on counting and verification.
Challenge and get performance evaluation