Practice - Conclusion and Summary
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Practice Questions
Test your understanding with targeted questions
Define a bipartite graph.
💡 Hint: Focus on how the vertices are organized.
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
What is the key requirement for a complete matching according to Hall's Marriage Theorem?
💡 Hint: Think about how many connections you need for job assignments.
True or False: Every maximum matching is also a maximal matching.
💡 Hint: Consider the definitions of both terms.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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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