Geodesic
A Note on the Uniqueness of Stable Marriage Matching
Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 49-55.

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In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.
Keywords: stable matching, Gale-Shapley model, stable perfect matching 
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Drgas-Burchardt, Ewa. A Note on the Uniqueness of Stable Marriage Matching. Discussiones Mathematicae. Graph Theory, Tome 33 (2013) no. 1, pp. 49-55. http://geodesic.mathdoc.fr/item/DMGT_2013_33_1_a4/

[1] E. Drgas-Burchardt and Z. Świtalski, A number of stable matchings in models of the Gale-Shapley type, manuscript.

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[6] D.E. Knuth, Mariages Stables (Less Presses de l’Universite de Montreal, Montreal, 1976).

[7] D.E. Knuth, Stable Marriage and Its Relation to other Combinatorial Problems. An Introduction to the Mathematical Analysis of Algorithms (American Mathematical Society, Providence, Rhode Island, 1997).