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

Practice: Conclusion and Summary

Lesson 25.2Introduction to Bipartite Graphs and Matching

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9 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a bipartite graph.
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Focus on how the vertices are organized.
Question 2.
What is a matching?
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Think about how edges can connect without overlapping.
3Question 3.
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.
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Think about how many connections you need for job assignments.
4Question 4.
True or False: Every maximum matching is also a maximal matching.
- True
- False
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Consider the definitions of both terms.
Question 5.
Given a bipartite graph with five jobs and only three employees, analyze whether a complete matching exists using Hall’s theorem.
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Check the neighbors for each subset of jobs.
Question 6.
Create your own example of a bipartite graph that demonstrates a maximum matching different from a complete matching.
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Include at least one unmatched vertex in your example.

5 more questions in this section. Enroll free to practise them all.