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2 cards from this section. Quick, good the night before a test.
Define a bipartite graph.
Think about how the vertices are organized in two distinct groups.
What is Hall's Marriage Theorem?
Consider its application in matching problems.
What ensures a complete matching exists in a bipartite graph?
Think about the relationship between vertices in different sets.
Hall's Marriage Theorem applies to which type of graphs?
Recall the definition of a bipartite graph.
Given a bipartite graph with 6 vertices in V₁ and 8 in V₂, five vertices in V₁ have enough neighbors in V₂ to meet Hall's condition, one does not, and one vertex in V₂ is left unmatched. Can a complete matching still be formed?
Evaluate the matching possibility based on the violating vertex.
Create an example of a bipartite graph that satisfies Hall's condition and show how to build a complete matching.
Draw the graph to visualize connections.
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