Popular Matchings of Desired Size.

Our input is an instance of the stable marriage problem with strict and possibly incomplete lists, i.e., it is a bipartite graph (G = (A cup B,E)) where each vertex has a strict preference list ranking its neighbors. We consider a generalization of stable matchings called popular matchings: a matching M in G is popular if there is no matching (Mu0027) such that the vertices that prefer (Mu0027) to M outnumber those that prefer M to (Mu0027).