This is Ágnes Cseh's talk "What is ... a stable marriage?" at the "What is ...?" seminar. The talk was given on Friday, November 5, 2010, 3:30pm at the BMS Loft at Urania.
This definitely important question can be answered with the help of graph theory. The stable marriage theorem of Gale and Shapley states that for some men and women there always exists a stable marriage scheme, that is, a set of pairs such that no man and woman mutually prefer each other to their partners in the matching. The stable marriage problem can be extended in several directions, one of the most recent topics deals with network flows. Besides sketching some theorems and unanswered questions we will give some useful hints to find a stable partner in real life.
For more "What is ...?" seminar videos, visit math.fu-berlin.de/w/Math/WhatIsSeminar