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2 cards from this section. Quick, good the night before a test.
Define a bipartite graph.
Think about the two distinct groups in the graph.
What does matching mean in the context of graphs?
Consider how you could pair up objects without overlap.
What is a bipartite graph?
Consider the definition and how vertices are arranged.
True or False: A complete matching always exists in every bipartite graph.
Think about conditions necessary for complete matching.
Given a bipartite graph with subsets U={1, 2, 3} and V={a, b} where U has preferences: 1-a, 1-b, 2-a, 3-a, determine if complete matching is possible.
Use Hall's theorem to check against preferences.
In a graph representing students to projects, students S={X, Y} can do projects P={1, 2, 3}. X can do 1 & 2, Y can do 2 & 3. Is there complete matching?
Analyze the connections using Hall's theorem conditions.
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