Hall's Condition
Given a set A, let N(A) be the set of neighbors of A. Then the bipartite graph G with bipartitions X and Y has a perfect matching iff |N(A)|>=|A| for all subsets A of X.
See also
Hall's Theorem, Marriage Theorem, Perfect MatchingThis entry contributed by Chris Heckman
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References
Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Referenced on Wolfram|Alpha
Hall's ConditionCite this as:
Heckman, Chris. "Hall's Condition." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HallsCondition.html