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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 organized.
What does a perfect match in a bipartite graph mean?
Consider what 'one-to-one' pairing means.
What is a bipartite graph?
Think about how vertices are paired.
True or False: A perfect matching requires that at least one vertex in the bipartite graph be left unmatched.
Relate this to the definition of 'perfect'.
Consider a school with 5 teachers: T1, T2, T3, T4, T5 and 4 courses: C1, C2, C3, C4. The preferences are as follows: T1 (C1, C2), T2 (C2, C3), T3 (C3), T4 (C1), T5 (C2, C4). Determine if a perfect matching exists and justify your answer.
Remember to evaluate all teachers' potential matches before concluding.
A university has to assign courses among 6 professors and 5 classes, where classes have specific capacity limits and professors have their preferences. Develop a flow network and find a maximum flow configuration that indicates potential assignments.
Keep track of the flow capacities while ensuring no professor is overloaded beyond their willing assignments.
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