Practice Conclusion And References (26.2) - Proof of Hall's Marriage Theorem
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Conclusion and References

Practice - Conclusion and References

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Practice Questions

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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.

4 more questions available

Interactive Quizzes

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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.

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Challenge Problems

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Challenge 1 Hard

Provided a bipartite graph, demonstrate the failure of the matching condition. What modifications would result in a valid matching?

💡 Hint: Analyze subsets closely.

Challenge 2 Hard

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.

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Reference links

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