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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a bipartite graph.
💡 Hint: Consider how edges connect the two sets.
Question 2
Easy
What is matching in a graph?
💡 Hint: Think about how edges connect vertices without overlap.
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 Hall's Marriage Theorem concerned with?
- The existence of cycles in graphs
- Conditions for complete matching in bipartite graphs
- The total number of edges in a graph
💡 Hint: Think about the relationships between vertices.
Question 2
True or False: Every maximal matching is also a maximum 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 sets {A, B, C} and {X, Y, Z}, where edges connect A-X, B-Y, and C-Z, devise a complete matching. What further connections can you construct to meet Hall's condition?
💡 Hint: Examine the size and distribution of edges.
Question 2
Consider a job assignment scenario: You have four jobs and only two employees capable of covering those roles. Why won't a complete assignment be attainable? Illustrate using Hall's theorem.
💡 Hint: Count the tasks versus available workers.
Challenge and get performance evaluation