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3 cards from this section. Quick, good the night before a test.
What is the necessary condition for Hall's Marriage Theorem?
Think about matches in pairs.
Define a complete matching in the context of bipartite graphs.
Consider pairs—everyone must find a match.
In a bipartite graph, what must be true for a complete matching to exist?
Think about matching and availability in pairs.
True or False: The proof for the sufficiency condition of Hall's theorem does not use induction.
Remember the steps we took in class.
Construct a bipartite graph with 5 vertices on one side and 3 on the other. Demonstrate whether a matching is possible based on the neighbor condition.
Draw edges based on connections.
Using Hall's theorem, evaluate a scenario where a group of 7 students is connected to exactly 5 tutors with specific matching pairs. Discuss if a complete matching exists or not.
Check each student's connections before concluding.
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