Stable roommates with free edges Kataŕına Cechlárová and Tamás Fleiner

In the well-known stable roommates problem we have given a graph with preferences on the stars and we are looking for a matching that is not blocked by a nonmatching edge. There are well-known algorithms to find such a matching or to conclude that no such matching exists. Here we consider a relaxed problem motivated by kidney exchanges, where not all edges of the graph can block a matching. We show that this problem is NP-complete and apply the result to give an alternative proof of an NP-completeness result of Ronn.