Three-dimensional Stable Matching with Cyclic Preferences

07/16/2018

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by   Kanstantsin Pashkovich, et al.

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We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. Despite extensive study of the problem by experts from different areas, the question of whether every instance of this problem admits a stable matching remains unanswered. 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, Sjöstrand 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.