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Practice Questions
Test your understanding with targeted questions related to the topic.
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.
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 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.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation