We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the "lone...

It is well-known that couples that look jointly for jobs in the same centralized labor market may cause instabilities. We demonstrate that for a natural preference domain for couples, namely the domain of responsive preferences, the existence of stable matchings can easily be established....

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative...