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2 cards from this section. Quick, good the night before a test.
Define a bipartite graph.
Consider how edges connect the two sets.
What is matching in a graph?
Think about how edges connect vertices without overlap.
What is Hall's Marriage Theorem concerned with?
Think about the relationships between vertices.
True or False: Every maximal matching is also a maximum matching.
Consider the definitions of both terms.
Given a bipartite graph with sets {A, B, C} and {X, Y, Z}, where edges connect A-X, B-Y, and C-Z, devise a complete matching. What further connections can you construct to meet Hall's condition?
Examine the size and distribution of edges.
Consider a job assignment scenario: You have four jobs and only two employees capable of covering those roles. Why won't a complete assignment be attainable? Illustrate using Hall's theorem.
Count the tasks versus available workers.
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