We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of...

We consider one-to-one matching (roommate) problems in which agents (students) can either be matched as pairs or remain single. The aim of this paper is twofold. First, we review a key result for roommate problems (the "lonely wolf" theorem) for which we provide a concise and elementary proof....