the existence of a transversal,
This essay focuses on the existence of a transversal, name comes from an application to matchmaking: given a list of potential matches among an equal number of brides
the existence of a transversal,
on a graphs question and need an explanation to help me understand better.
Proof problems about Menger’s theorem and Hall’s theorem. I have attached notes to help you out. I need 80%+ only bid if you can do this. Thank you.
The name comes from an application to matchmaking: given a list of potential matches among an equal number of brides and grooms, the theorem gives a necessary and sufficient condition on the list for everyone to be married to an agreeable match.
Suppose there are n women and n men, all of whom want to get married to someone of the opposite sex. Suppose further that the women each have a list of the men. They would be happy to marry, and that every man would be happy to marry any woman. This is who is happy to marry him, and that each person can only have one spouse.
In this case, Hall’s marriage theorem says that the men and women. This can all be paired off in marriage so that everyone is happy, if and only if the marriage condition
The condition given in the theorem is clearly necessary for the existence of a transversal, because any transversal must include |R| distinct elements from the sets in R, so those sets must together contain at least |R| elements.
(2) The condition given in the theorem is generally called the “marriage condition.” So Hall’s Marriage Theorem says that S has a transversal if and only if it satisfies the marriage condition.
Application to
Details;
Firstly, be keen
secondly, be honest
