If a group of men and women may date only if they have previously been introduced, then a complete set of dates is possible iff every subset of men has collectively been introduced to at least as many women, and vice versa (Hall 1935; Chartrand 1985, p. 121; Skiena 1990, p. 240).

# Marriage Theorem

## See also

Matching## Explore with Wolfram|Alpha

## References

Chartrand, G.*Introductory Graph Theory.*New York: Dover, 1985.Hall, P. "On Representatives of Subsets."

*J. London Math. Soc.*

**10**, 26-30, 1935.Skiena, S.

*Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica.*Reading, MA: Addison-Wesley, 1990.

## Referenced on Wolfram|Alpha

Marriage Theorem## Cite this as:

Weisstein, Eric W. "Marriage Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/MarriageTheorem.html