Practice Conclusion And Summary (25.2) - Introduction to Bipartite Graphs and Matching
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Conclusion and Summary

Practice - Conclusion and Summary

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Practice Questions

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Question 1 Easy

Define a bipartite graph.

💡 Hint: Focus on how the vertices are organized.

Question 2 Easy

What is a matching?

💡 Hint: Think about how edges can connect without overlapping.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the key requirement for a complete matching according to Hall's Marriage Theorem?

Each vertex in the first set must be matched to a unique vertex in the second set.
The neighbors count must be at least equal to the number of vertices in any chosen subset.
All edges must create cycles.

💡 Hint: Think about how many connections you need for job assignments.

Question 2

True or False: Every maximum matching is also a maximal matching.

True
False

💡 Hint: Consider the definitions of both terms.

1 more question available

Challenge Problems

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Challenge 1 Hard

Given a bipartite graph with five jobs and only three employees, analyze whether a complete matching exists using Hall’s theorem.

💡 Hint: Check the neighbors for each subset of jobs.

Challenge 2 Hard

Create your own example of a bipartite graph that demonstrates a maximum matching different from a complete matching.

💡 Hint: Include at least one unmatched vertex in your example.

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