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3 cards from this section. Quick, good the night before a test.
Define a bipartite graph.
Focus on the structure and edges of the graph.
What is matching in the context of bipartite graphs?
Think about how tasks can be assigned without overlaps.
A matching in a bipartite graph must ensure that:
Think about the core definition of matching.
True or False: A maximum matching can be a maximal matching.
Consider how 'maximum' and 'maximal' are defined.
Consider a bipartite graph with 5 employees and 3 tasks. If two employees can do all tasks but one, and the rest of employees can do none, explain how a complete matching might work.
Map each employee’s preferences to visualize the match.
Create a bipartite graph that illustrates the failure of Hall’s condition. What implications does this have for completing a matching?
Identify subsets and neighbors for rigorous analysis.
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