Practice - Theorem Statement and Necessary Condition
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Practice Questions
Test your understanding with targeted questions
Define a bipartite graph.
💡 Hint: Think about how vertices are separated.
What does it mean for a graph to have a complete matching?
💡 Hint: Imagine pairing a group of boys and girls at a dance.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main condition of Hall's Marriage Theorem?
💡 Hint: Think about neighbor requirements for matching.
If there exists a complete matching, can we say Hall's condition holds?
💡 Hint: Consider how matching pairs must work.
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Challenge Problems
Push your limits with advanced challenges
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.
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.
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