Practice - Case 1: k-sized Subset with More Neighbours
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Practice Questions
Test your understanding with targeted questions
What is a bipartite graph?
💡 Hint: Think about how the vertices are connected.
Define a complete matching.
💡 Hint: Consider what it means to cover all vertices in one set.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Hall's Marriage Theorem state?
💡 Hint: Consider what it means for subsets and their neighbours.
True or False: If |N(A)| < |A| for any subset A, a complete matching can exist.
💡 Hint: Think about how many vertices need to be matched.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Prove Hall’s Marriage Theorem using a specific bipartite graph example and calculating neighbours.
💡 Hint: Draw the bipartite graph and label neighbours.
Construct different bipartite graphs, varying the connections, and identify which meet or violate Hall’s conditions.
💡 Hint: Compare neighbour counts with set sizes.
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