Practice - Hall's Marriage Theorem
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Define a bipartite graph.
💡 Hint: Consider how edges connect the two sets.
What is matching in a graph?
💡 Hint: Think about how edges connect vertices without overlap.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is Hall's Marriage Theorem concerned with?
💡 Hint: Think about the relationships between vertices.
True or False: Every maximal matching is also a maximum 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 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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.