Three-dimensional stable matching with cyclic preferences

We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. In 2004, Boros, Gurvich, Jaslar and Krasner showed that a stable matching always exists when the number of agents in each of the groups is three. In 2006, Eriksson, Sjostrand and Strimling showed that a stable matching exists also when the number of agents in each group is four. In this paper, we demonstrate that a stable matching exists when each group has five agents. Furthermore, we show that there are at least two distinct stable matchings in that setting.