Abstract
The stable marriage problem (SMP) is a combinatorial problem to find stable matching between n women and n men given a complete preference list of men over women and vice versa. An instance of the SMP can be expressed by a bipartite graph with multiple (weighted) edges. By rearranging the graph, we use a diagram that involves several constraints to visualize several symmetries. By the diagram, all instances of the size-three SMP (three women and three men) are classified. The classification may be supported by the fact that the same class has the same stable matching.
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Hayashi, T., Hata, Y. & Ishida, Y. A diagrammatic classification in a combinatorial problem: the case of the stable marriage problem. Artif Life Robotics 16, 575–579 (2012). https://doi.org/10.1007/s10015-011-0993-x
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DOI: https://doi.org/10.1007/s10015-011-0993-x