Practice - Types of Matching
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Practice Questions
Test your understanding with targeted questions
Define a bipartite graph.
💡 Hint: Focus on the structure and edges of the graph.
What is matching in the context of bipartite graphs?
💡 Hint: Think about how tasks can be assigned without overlaps.
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Interactive Quizzes
Quick quizzes to reinforce your learning
A matching in a bipartite graph must ensure that:
💡 Hint: Think about the core definition of matching.
True or False: A maximum matching can be a maximal matching.
💡 Hint: Consider how 'maximum' and 'maximal' are defined.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Consider a bipartite graph with 5 employees and 3 tasks. If two employees can do all tasks but one, and the rest of employees can do none, explain how a complete matching might work.
💡 Hint: Map each employee’s preferences to visualize the match.
Create a bipartite graph that illustrates the failure of Hall’s condition. What implications does this have for completing a matching?
💡 Hint: Identify subsets and neighbors for rigorous analysis.
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Reference links
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