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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a bipartite graph.
💡 Hint: Think about how vertices are separated.
Question 2
Easy
What does it mean for a graph to have a complete matching?
💡 Hint: Imagine pairing a group of boys and girls at a dance.
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 the main condition of Hall's Marriage Theorem?
- |N(A)| < |A|
- |N(A)| = |A|
- |N(A)| ≥ |A|
💡 Hint: Think about neighbor requirements for matching.
Question 2
If there exists a complete matching, can we say Hall's condition holds?
- True
- False
💡 Hint: Consider how matching pairs must work.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a bipartite graph where V1 = {v1, v2, v3} and V2 = {u1, u2}. If v1 is connected to both u1 and u2, and v2 is only connected to u1, while v3 is connected to both. Determine if a complete matching exists.
💡 Hint: Count pairs and check connections.
Question 2
Design a bipartite graph that satisfies Hall's condition but does not allow for a complete matching. Explain how.
💡 Hint: Think of how connections can visually appear.
Challenge and get performance evaluation