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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 the structure and edges of the graph.
Question 2
Easy
What is matching in the context of bipartite graphs?
💡 Hint: Think about how tasks can be assigned without overlaps.
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
A matching in a bipartite graph must ensure that:
- No edges share a vertex.
- All vertices are included in the matching.
- Each vertex can handle multiple jobs.
💡 Hint: Think about the core definition of matching.
Question 2
True or False: A maximum matching can be a maximal matching.
- True
- False
💡 Hint: Consider how 'maximum' and 'maximal' are defined.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation