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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the necessary condition for Hall's Marriage Theorem?
💡 Hint: Think about matches in pairs.
Question 2
Easy
Define a complete matching in the context of bipartite graphs.
💡 Hint: Consider pairs—everyone must find a match.
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
In a bipartite graph, what must be true for a complete matching to exist?
- |N(A)| < |A|
- |N(A)| = |A|
- |N(A)| ≥ |A|
💡 Hint: Think about matching and availability in pairs.
Question 2
True or False: The proof for the sufficiency condition of Hall's theorem does not use induction.
- True
- False
💡 Hint: Remember the steps we took in class.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Construct a bipartite graph with 5 vertices on one side and 3 on the other. Demonstrate whether a matching is possible based on the neighbor condition.
💡 Hint: Draw edges based on connections.
Question 2
Using Hall's theorem, evaluate a scenario where a group of 7 students is connected to exactly 5 tutors with specific matching pairs. Discuss if a complete matching exists or not.
💡 Hint: Check each student's connections before concluding.
Challenge and get performance evaluation