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2 cards from this section. Quick, good the night before a test.
Define a bipartite graph.
Think about how vertices are separated.
What does it mean for a graph to have a complete matching?
Imagine pairing a group of boys and girls at a dance.
What is the main condition of Hall's Marriage Theorem?
Think about neighbor requirements for matching.
If there exists a complete matching, can we say Hall's condition holds?
Consider how matching pairs must work.
Given a bipartite graph where V1 = {v1, v2, v3} and V2 = {u1, u2}. If v1 is connected to both u1 and u2, and v2 is only connected to u1, while v3 is connected to both. Determine if a complete matching exists.
Count pairs and check connections.
Design a bipartite graph that satisfies Hall's condition but does not allow for a complete matching. Explain how.
Think of how connections can visually appear.
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