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4 cards from this section. Quick, good the night before a test.
What defines a bipartite graph?
Think about the two-group structure.
Why can't teachers be matched to courses they don't prefer?
Consider teacher qualifications.
What characterizes a bipartite graph?
Refer back to the definition.
True or False: In a bipartite graph, teachers can teach courses they initially didn't prefer.
Think about the consequences of misallocation.
Given a bipartite graph of 3 teachers (T1, T2, T3) and 5 courses (C1 to C5), with the following preferences: T1(C1, C2), T2(C2, C3), T3(C4, C5). Determine if a perfect matching is possible.
Consider the number of vertices in both sets.
Modify the graph from the previous problem to include a preference for T1 to teach C2 and C3. Analyze the impact on perfect matching.
Think about how additional edges affect matching possibilities.
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