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Hall's Theorem


There exists a system of distinct representatives for a family of sets S_1, S_2, ..., S_m iff the union of any k of these sets contains at least k elements for all k from 1 to m (Harary 1994, p. 53).


See also

Hall's Condition

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References

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.

Referenced on Wolfram|Alpha

Hall's Theorem

Cite this as:

Weisstein, Eric W. "Hall's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HallsTheorem.html

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